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Paper Citation Record · LEDGER

On the optimal Sobolev threshold for evolution equations with rough nonlinearities

As of 14 August 2026, this Paper Citation Record lists 67 of 67 outbound references and 0 inbound Pith citation observations for arXiv:2505.14966.

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pith.paper-citation-record.v1
2505.14966 v1

Coverage vector

measured 67 of 67 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-07T15:34:55.958848Z

measured 67 of 67 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-14T06:32:32.682623+00:00

measured 0 of 0 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links

measured 0 of 1 external citation measurements

A source-named dated measurement, never combined with another source.

Source: cited_works

Reference resolution

67 of 67 outbound references displayed

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External citation measurements

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Outbound references

Observation b18328f4-8ff2-460f-b608-26436d79ebea · outbound

This paper cites Calcul symbolique et propagation des singular it´ es pour les ´ equations aux d´ eriv´ ees partielles non lin´ eaires.Ann.

On the optimal Sobolev threshold for evolution equations with rough nonlinearities Calcul symbolique et propagation des singular it´ es pour les ´ equations aux d´ eriv´ ees partielles non lin´ eaires.Ann

Reference 1

Resolution
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Observation e64f42bc-39c3-47b3-9417-090964b66e02 · outbound

This paper cites A sharpness result for powers of Besov fu nctions.

On the optimal Sobolev threshold for evolution equations with rough nonlinearities A sharpness result for powers of Besov fu nctions

Reference 2

Resolution
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Source-reported events for the cited work

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Observation 880662ec-519c-4159-9218-2b81c67cd503 · outbound

This paper cites Fonctions qui op` erent sur les espaces de Sobolev.

On the optimal Sobolev threshold for evolution equations with rough nonlinearities Fonctions qui op` erent sur les espaces de Sobolev

Reference 3

Resolution
verified fuzzy
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Source-reported events for the cited work

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Observation 6e936e3a-a6f4-4fc3-8ca5-49cbd45d3f97 · outbound

This paper cites Compos ition operators on Lizorkin-Triebel spaces.

On the optimal Sobolev threshold for evolution equations with rough nonlinearities Compos ition operators on Lizorkin-Triebel spaces

Reference 4

Resolution
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Source-reported events for the cited work

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Observation d3f05f3d-d836-4dfb-8c7a-6f560f830aff · outbound

This paper cites Compos ition operators acting on Besov spaces on the real line.

On the optimal Sobolev threshold for evolution equations with rough nonlinearities Compos ition operators acting on Besov spaces on the real line

Reference 5

Resolution
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Source-reported events for the cited work

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Observation d4a4afca-ccbf-4f0f-8ec5-033743aab57b · outbound

This paper cites On nonlinear Schr¨ odinger equations.

On the optimal Sobolev threshold for evolution equations with rough nonlinearities On nonlinear Schr¨ odinger equations

Reference 6

Resolution
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Source-reported events for the cited work

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Observation f62cda17-b35b-4852-8d88-16eb22e07520 · outbound

This paper cites Scattering in the energy space and below for 3D N LS.

On the optimal Sobolev threshold for evolution equations with rough nonlinearities Scattering in the energy space and below for 3D N LS

Reference 7

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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

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Observation 086c77a6-9524-438f-b868-caee7c954983 · outbound

This paper cites Global solutions of nonlinear Schr¨ odinger equations, volume 46 of American Mathematical Society Colloquium Publications.

On the optimal Sobolev threshold for evolution equations with rough nonlinearities Global solutions of nonlinear Schr¨ odinger equations, volume 46 of American Mathematical Society Colloquium Publications

Reference 8

Resolution
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Source-reported events for the cited work

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Observation f5d4a362-8f55-4d0c-93bc-55352f7c7b93 · outbound

This paper cites On the global Cauchy problem for the nonlinear Sc hr¨ odinger equation.Proc.

On the optimal Sobolev threshold for evolution equations with rough nonlinearities On the global Cauchy problem for the nonlinear Sc hr¨ odinger equation.Proc

Reference 9

Resolution
verified fuzzy
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Source-reported events for the cited work

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Observation 7c655979-1540-47e9-bf6b-a2b32bfc24c4 · outbound

This paper cites Construction of blowup solu tions for the nonlinear Schr¨ odinger equation with critical nonlinearity.

On the optimal Sobolev threshold for evolution equations with rough nonlinearities Construction of blowup solu tions for the nonlinear Schr¨ odinger equation with critical nonlinearity

Reference 10

Resolution
verified fuzzy
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Source-reported events for the cited work

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Observation cc0ed2b4-42cd-4234-9ce0-3ac9b6278828 · outbound

This paper cites an unresolved cited work.

On the optimal Sobolev threshold for evolution equations with rough nonlinearities Unresolved cited work

Reference 11

Resolution
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Observation 253520b5-b707-4aa5-bb11-5dee7a74fdc7 · outbound

This paper cites Semilinear Schr¨ odinger equations, volume 10 of Courant Lecture Notes in Mathematics.

On the optimal Sobolev threshold for evolution equations with rough nonlinearities Semilinear Schr¨ odinger equations, volume 10 of Courant Lecture Notes in Mathematics

Reference 12

Resolution
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Source-reported events for the cited work

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Observation 59006764-10ae-4eb9-b669-a1ae992947d1 · outbound

This paper cites Weissler.

On the optimal Sobolev threshold for evolution equations with rough nonlinearities Weissler

Reference 13

Resolution
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Source-reported events for the cited work

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Observation 0fb70b7b-7764-4ddd-b166-b2135df82385 · outbound

This paper cites Continuous dependence for NLS in fractional order spaces.

On the optimal Sobolev threshold for evolution equations with rough nonlinearities Continuous dependence for NLS in fractional order spaces

Reference 14

Resolution
verified fuzzy
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Source-reported events for the cited work

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Observation 1a63cf92-90b8-4f85-8541-eefb773f72de · outbound

This paper cites Local well-p osedness for the H 2-critical nonlinear Schr¨ odinger equation.

On the optimal Sobolev threshold for evolution equations with rough nonlinearities Local well-p osedness for the H 2-critical nonlinear Schr¨ odinger equation

Reference 15

Resolution
verified fuzzy
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

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Observation c3cec1d9-2a41-4f7c-85bf-dba17d33b2f6 · outbound

This paper cites Local existence, global e xistence, and scattering for the nonlinear Schr¨ odinger equation.Commun.

On the optimal Sobolev threshold for evolution equations with rough nonlinearities Local existence, global e xistence, and scattering for the nonlinear Schr¨ odinger equation.Commun

Reference 16

Resolution
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Source-reported events for the cited work

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Observation 25898bf3-5258-4873-9e8d-b88ed01565d7 · outbound

This paper cites Spatial behavior for NLS a nd applications to scattering.

On the optimal Sobolev threshold for evolution equations with rough nonlinearities Spatial behavior for NLS a nd applications to scattering

Reference 17

Resolution
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Source-reported events for the cited work

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Observation aee573a9-714a-46d5-a53e-739a4a325933 · outbound

This paper cites Local smooth solutions of the nonlinear Klein-Gordon equation.

On the optimal Sobolev threshold for evolution equations with rough nonlinearities Local smooth solutions of the nonlinear Klein-Gordon equation

Reference 18

Resolution
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Source-reported events for the cited work

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Observation b4eef0a9-3714-4414-9899-5e53225ef614 · outbound

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On the optimal Sobolev threshold for evolution equations with rough nonlinearities Unresolved cited work

Reference 19

Resolution
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Source-reported events for the cited work

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This paper cites Ill-posedness for nonlinear Schrodinger and wave equations.

On the optimal Sobolev threshold for evolution equations with rough nonlinearities Ill-posedness for nonlinear Schrodinger and wave equations

Reference 20

Resolution
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Source-reported events for the cited work

Unavailable: canonical work link unavailable.

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Observation b27ffca4-7a48-47d6-9a34-572fcc9ae85f · outbound

This paper cites Polynomial upper bounds for the instability of the nonlinear Schr¨ odinger equation below the e nergy norm.

On the optimal Sobolev threshold for evolution equations with rough nonlinearities Polynomial upper bounds for the instability of the nonlinear Schr¨ odinger equation below the e nergy norm

Reference 21

Resolution
verified fuzzy
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Source-reported events for the cited work

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Observation 8f973825-7f4a-471c-8842-cd2cb111a780 · outbound

This paper cites Blow-up criteria for fractional nonlinear Schr¨ odinger equations.

On the optimal Sobolev threshold for evolution equations with rough nonlinearities Blow-up criteria for fractional nonlinear Schr¨ odinger equations

Reference 22

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T15:34:56.577231Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

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Observation 79a2b158-c77a-4eeb-9bc4-c25da5ffeccd · outbound

This paper cites On the well-posedness for NLS in H s.

On the optimal Sobolev threshold for evolution equations with rough nonlinearities On the well-posedness for NLS in H s

Reference 23

Resolution
verified fuzzy
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

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Observation b79277c9-a268-4441-ab88-879fd181869a · outbound

This paper cites Well-posedness and dynamics of solutions to the generalized KdV with low power nonlinearity.

On the optimal Sobolev threshold for evolution equations with rough nonlinearities Well-posedness and dynamics of solutions to the generalized KdV with low power nonlinearity

Reference 24

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T15:34:56.553856Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

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Observation 0595163c-e318-43a6-b865-fd74e34e4ff5 · outbound

This paper cites The Kato-Ponce inequality.

On the optimal Sobolev threshold for evolution equations with rough nonlinearities The Kato-Ponce inequality

Reference 25

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T15:34:56.541796Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

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Observation f21a1b38-4832-4d8c-a5d5-8da8a0b6f909 · outbound

This paper cites Sharp w ell-posedness for the cubic NLS and mKdV in H s(R).

On the optimal Sobolev threshold for evolution equations with rough nonlinearities Sharp w ell-posedness for the cubic NLS and mKdV in H s(R)

Reference 26

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T15:34:56.529644Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

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Observation 1d9c4416-d64c-4eb8-abba-90e02370bf92 · outbound

This paper cites On dispersive blow-ups for t he nonlinear Schr¨ odinger equation.Differential Integral Equations, 29(9-10):875–888, 2016.

On the optimal Sobolev threshold for evolution equations with rough nonlinearities On dispersive blow-ups for t he nonlinear Schr¨ odinger equation.Differential Integral Equations, 29(9-10):875–888, 2016

Reference 27

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T15:34:56.517202Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

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Observation fd9299f6-4771-4f09-a33b-ca00f001bb9e · outbound

This paper cites Global solutions for cubic quasilinear ultrahyperbolic Schr\"odinger flows.

On the optimal Sobolev threshold for evolution equations with rough nonlinearities Global solutions for cubic quasilinear ultrahyperbolic Schr\"odinger flows

Reference 28

Resolution
verified exact
local_arxiv, observed 2026-08-07T15:34:56.023628Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

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Observation c97fa2a8-abb7-4f68-8396-fbcfbb76fd29 · outbound

This paper cites Local well-posedness for quas i-linear problems: a primer.

On the optimal Sobolev threshold for evolution equations with rough nonlinearities Local well-posedness for quas i-linear problems: a primer

Reference 29

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T15:34:56.503454Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

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Observation 181007eb-aa1b-4b87-8114-f6c6c56607fe · outbound

This paper cites Global solutions for cubic quasilinear Schroedinger flows in two and higher dimensions.

On the optimal Sobolev threshold for evolution equations with rough nonlinearities Global solutions for cubic quasilinear Schroedinger flows in two and higher dimensions

Reference 30

Resolution
unresolved
no resolver link, observed 2026-08-07T15:34:55.802175Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

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Observation 082c88e3-6295-4eca-b92d-2eb7df0d131b · outbound

This paper cites On the boundedness of the mapping f ↦→ |f |µ , µ > 1 on Besov spaces.

On the optimal Sobolev threshold for evolution equations with rough nonlinearities On the boundedness of the mapping f ↦→ |f |µ , µ > 1 on Besov spaces

Reference 31

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T15:34:56.489345Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

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Observation eedf200e-4464-4e02-845e-f97c1d373f8e · outbound

This paper cites On nonlinear Schr¨ odinger equations.

On the optimal Sobolev threshold for evolution equations with rough nonlinearities On nonlinear Schr¨ odinger equations

Reference 32

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T15:34:56.476550Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

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Observation 40d4f2bf-bba4-41cd-9147-0a671e6c108d · outbound

This paper cites Nonlinear Schr¨ odinger equations.

On the optimal Sobolev threshold for evolution equations with rough nonlinearities Nonlinear Schr¨ odinger equations

Reference 33

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T15:34:56.464739Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

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Observation 29327448-0a09-410e-84bc-0a75038a7033 · outbound

This paper cites Kenig and Kenneth D.

On the optimal Sobolev threshold for evolution equations with rough nonlinearities Kenig and Kenneth D

Reference 34

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T15:34:56.451746Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

source=pdf_text observed=2026-08-07T15:34:55.820191Z digest=sha256:719991739505f98f41fcbfbd610e70220f870e0d2264c03ea8b40e1b99737e78

Observation 74e8c2d2-8cd6-4600-bad4-9a67312d07b0 · outbound

This paper cites Kenig, Gustavo Ponce, and Luis Vega.

On the optimal Sobolev threshold for evolution equations with rough nonlinearities Kenig, Gustavo Ponce, and Luis Vega

Reference 35

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T15:34:56.437143Z

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No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

source=pdf_text observed=2026-08-07T15:34:55.825112Z digest=sha256:aebfbf8316dfb41a239f95892a38c26d406c1899e89c25d38c6368564565b1fc

Observation 0aa1c88f-48e4-40d6-b43b-3c9edcea98d5 · outbound

This paper cites Kenig and Hideo Takaoka.

On the optimal Sobolev threshold for evolution equations with rough nonlinearities Kenig and Hideo Takaoka

Reference 36

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T15:34:56.421871Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

source=pdf_text observed=2026-08-07T15:34:55.829925Z digest=sha256:a534c6afe33252876b04fa5b52751e6b786d6b50a9ed5af5885316d315880059

Observation 3ed5e5ba-4f6c-41db-80e2-f49d98331dc7 · outbound

This paper cites KdV is well-posed in H − 1.

On the optimal Sobolev threshold for evolution equations with rough nonlinearities KdV is well-posed in H − 1

Reference 37

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T15:34:56.408349Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

source=pdf_text observed=2026-08-07T15:34:55.834140Z digest=sha256:333efe834b8f79189edad8d0bf19368178c5892d572f2485cb941dc701830397

Observation ba272e88-99e3-4d27-bb83-7460cf3383bd · outbound

This paper cites Energy-supercritical NLS: critical ˙H s-bounds imply scattering.

On the optimal Sobolev threshold for evolution equations with rough nonlinearities Energy-supercritical NLS: critical ˙H s-bounds imply scattering

Reference 38

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T15:34:56.394683Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

source=pdf_text observed=2026-08-07T15:34:55.838114Z digest=sha256:26bed6742a3e808aea5aae362a38aaf9860f75077be775e5d1adbd50695c342a

Observation 8bf87225-1730-4463-9b84-ab53d38a46f5 · outbound

This paper cites The radial defocusing energy-supe rcritical nonlinear wave equation in all space dimensions.

On the optimal Sobolev threshold for evolution equations with rough nonlinearities The radial defocusing energy-supe rcritical nonlinear wave equation in all space dimensions

Reference 39

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T15:34:56.381562Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

source=pdf_text observed=2026-08-07T15:34:55.842217Z digest=sha256:f01338312ea455b5d8d50cbde02d95d37174dbba96cde576e595b759e9972065

Observation 973f1bc9-f63b-4393-bd87-468e966f4b15 · outbound

This paper cites Sharp Lr asymptotics of the small solutions to the nonlinear Schr¨ odinger eq uations.

On the optimal Sobolev threshold for evolution equations with rough nonlinearities Sharp Lr asymptotics of the small solutions to the nonlinear Schr¨ odinger eq uations

Reference 40

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T15:34:56.368562Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

source=pdf_text observed=2026-08-07T15:34:55.846186Z digest=sha256:31d200874a3eaf4e969c925c31d1adf673510289aebdebf76bc7fcbde3aab42f

Observation 353d07d2-00c7-4e49-a143-f780f371b604 · outbound

This paper cites Une extension du th´ eor` eme de Bourdaud-Kateb-Meyer.

On the optimal Sobolev threshold for evolution equations with rough nonlinearities Une extension du th´ eor` eme de Bourdaud-Kateb-Meyer

Reference 41

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T15:34:56.357023Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

source=pdf_text observed=2026-08-07T15:34:55.851225Z digest=sha256:044f4f2f11a54e9509efb7b24448248ae028282e34cc6f9f0528f2b0adb0ce5d

Observation 7f2f3a4c-d612-428f-bc23-01c78a5ab3b8 · outbound

This paper cites an unresolved cited work.

On the optimal Sobolev threshold for evolution equations with rough nonlinearities Unresolved cited work

Reference 42

Resolution
unresolved
raw_fallback, observed 2026-08-07T15:34:56.345183Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

source=pdf_text observed=2026-08-07T15:34:55.855900Z digest=sha256:8d26d5d801674d9dca26688d91e29c599a8d09a4038d224840453606531d75c1

Observation 211391d2-da01-4bb3-b170-e6ad58b1883d · outbound

This paper cites Interpolation theory , volume 16 of Appunti.

On the optimal Sobolev threshold for evolution equations with rough nonlinearities Interpolation theory , volume 16 of Appunti

Reference 43

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T15:34:56.333827Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

source=pdf_text observed=2026-08-07T15:34:55.859687Z digest=sha256:3ed30fc2d7a31cb0af9fe3075f40870cef2f81aaae3dbcd864f76ef7397c152d

Observation 4dc5f108-d8cb-4dc6-bdf3-a25eccd108ad · outbound

This paper cites Marzuola, Jason Metcalfe, and Daniel Tataru.

On the optimal Sobolev threshold for evolution equations with rough nonlinearities Marzuola, Jason Metcalfe, and Daniel Tataru

Reference 44

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T15:34:56.320907Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

source=pdf_text observed=2026-08-07T15:34:55.864054Z digest=sha256:ffca98ef7ad94ce2a02cc0de3cdd9dc97020f9ffcc2e152aac63d01f1cc61c06

Observation 69a8541f-4cc4-4b54-959c-60fa6cfc249a · outbound

This paper cites Edizioni della Normale, Pisa, 2008.

On the optimal Sobolev threshold for evolution equations with rough nonlinearities Edizioni della Normale, Pisa, 2008

Reference 45

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T15:34:56.308261Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

source=pdf_text observed=2026-08-07T15:34:55.869099Z digest=sha256:e05adc9a65eb998caf0db285fb9e5e0139aa73f0f022895f01a11b8aefa030f8

Observation 271aa2ba-1783-4390-b33b-3b5028acdd02 · outbound

This paper cites On the regularity of the semilinear term on th e Cauchy problem for the Schr¨ odinger equa- tion.

On the optimal Sobolev threshold for evolution equations with rough nonlinearities On the regularity of the semilinear term on th e Cauchy problem for the Schr¨ odinger equa- tion

Reference 46

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T15:34:56.296856Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

source=pdf_text observed=2026-08-07T15:34:55.873761Z digest=sha256:238274dfff806f9bc30b1c62613f28387607023a8ea766a1482bb0758e6c0cf6

Observation 3f21c96f-e8d1-4b56-8899-a610f05bb35d · outbound

This paper cites Modified Strichartz estim ates with an application to the critical nonlinear Schr¨ odinger equation.Nonlinear Anal., 130:138–156, 2016.

On the optimal Sobolev threshold for evolution equations with rough nonlinearities Modified Strichartz estim ates with an application to the critical nonlinear Schr¨ odinger equation.Nonlinear Anal., 130:138–156, 2016

Reference 47

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T15:34:56.284355Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

source=pdf_text observed=2026-08-07T15:34:55.877635Z digest=sha256:0f0007fddb88a07b6ee822b8dc3148aed91f288b65cd6209b3a714a4161a265e

Observation 1b15a9d9-bddd-4ccb-80ce-7ef12c1755b3 · outbound

This paper cites Strichartz type estimat es in mixed Besov spaces with application to critical nonlinear Schr¨ odinger equations.J.

On the optimal Sobolev threshold for evolution equations with rough nonlinearities Strichartz type estimat es in mixed Besov spaces with application to critical nonlinear Schr¨ odinger equations.J

Reference 48

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T15:34:56.272746Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

source=pdf_text observed=2026-08-07T15:34:55.881674Z digest=sha256:a3a7e9418cab57b430f9a2ed48108ebe8610492146a3a63e7d5dd8265692d90f

Observation 9efb4997-a13a-455a-8e98-dd554fe5df64 · outbound

This paper cites On the boundedness of the mapping f → |f | in Besov spaces.

On the optimal Sobolev threshold for evolution equations with rough nonlinearities On the boundedness of the mapping f → |f | in Besov spaces

Reference 49

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T15:34:56.261053Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

source=pdf_text observed=2026-08-07T15:34:55.886334Z digest=sha256:a5a84ea8f87fd29ecaf24ecae6f165cfb816e89f8c68e0edfafb772810cb05cd

Observation 21d944a8-0283-43d2-86a9-eb81e1267a9d · outbound

This paper cites Local solutions of semilinear wave equations in H s+1.

On the optimal Sobolev threshold for evolution equations with rough nonlinearities Local solutions of semilinear wave equations in H s+1

Reference 50

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T15:34:56.248722Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

source=pdf_text observed=2026-08-07T15:34:55.890121Z digest=sha256:00c11ddc09c1b5daf09a6be001023efccf2ef042f1c187d055159ce2985395d4

Observation 2adabcd9-8217-4fce-b5cc-cff031a233c1 · outbound

This paper cites Solutions of semilinear Schr¨ odinger equation s in H s.

On the optimal Sobolev threshold for evolution equations with rough nonlinearities Solutions of semilinear Schr¨ odinger equation s in H s

Reference 51

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T15:34:56.236602Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

source=pdf_text observed=2026-08-07T15:34:55.893892Z digest=sha256:3226d7bd7dd216a800d94ecd52b57241e48377a6c3c762c1b843f5ece8a8a923

Observation 84a3c17c-0784-461a-aebb-e5b95e177ca0 · outbound

This paper cites an unresolved cited work.

On the optimal Sobolev threshold for evolution equations with rough nonlinearities Unresolved cited work

Reference 52

Resolution
unresolved
raw_fallback, observed 2026-08-07T15:34:56.221953Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

source=pdf_text observed=2026-08-07T15:34:55.897772Z digest=sha256:183eb067c08f737b931b897a8792093956486254d340265751abaacd6c3fb258

Observation 6c514806-2129-4c9c-9a7a-afb837bca791 · outbound

This paper cites an unresolved cited work.

On the optimal Sobolev threshold for evolution equations with rough nonlinearities Unresolved cited work

Reference 53

Resolution
verified exact
doi, observed 2026-08-07T15:34:55.993515Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

source=pdf_text observed=2026-08-07T15:34:55.901165Z digest=sha256:a9de67124d3c630ef12588e1db7d4c1b07b4c83cb4a38c734e43a8dc3ff2688f

Observation 07969c69-3882-47b9-bb02-bd3f74da586b · outbound

This paper cites On Low Regularity Dynamics for Quasilinear Dispersive Equa tions and Free Boundary Problems.

On the optimal Sobolev threshold for evolution equations with rough nonlinearities On Low Regularity Dynamics for Quasilinear Dispersive Equa tions and Free Boundary Problems

Reference 54

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T15:34:56.209872Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

source=pdf_text observed=2026-08-07T15:34:55.905302Z digest=sha256:d30a3b8d6aa8f46d3391fc5d793daa450be7ab2df466a9d2318491f242fadf01

Observation 014b270f-b9db-4d2c-b4d9-1c834bed2689 · outbound

This paper cites Strichartz.

On the optimal Sobolev threshold for evolution equations with rough nonlinearities Strichartz

Reference 55

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T15:34:56.198463Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

source=pdf_text observed=2026-08-07T15:34:55.909128Z digest=sha256:b875122f2df7d5c0aa15760ac8af264ee10e529817f7a71a3060c61dee0dd630

Observation 02035a4d-7db0-44f4-8d28-844e0331bac6 · outbound

This paper cites The nonlinear Schr¨ odinger equation: self-focusing and wa ve collapse , volume 139.

On the optimal Sobolev threshold for evolution equations with rough nonlinearities The nonlinear Schr¨ odinger equation: self-focusing and wa ve collapse , volume 139

Reference 56

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T15:34:56.186443Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

source=pdf_text observed=2026-08-07T15:34:55.912508Z digest=sha256:db33906e6b2265dacecfbe50a679dafde9b78b9b3fed1ae1b740ef011800002d

Observation 2882b3c9-b1ca-4ae4-b0ea-47b39d4be435 · outbound

This paper cites On local well-posedness for H s-critical nonlinear Schr¨ odinger equations.

On the optimal Sobolev threshold for evolution equations with rough nonlinearities On local well-posedness for H s-critical nonlinear Schr¨ odinger equations

Reference 57

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T15:34:56.174674Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

source=pdf_text observed=2026-08-07T15:34:55.917110Z digest=sha256:2bd16722b9cd481648f4178285f0e08a65ba22d723d1db0c251200b203b8cba1

Observation e7a904e5-ffc2-4dc9-a3b0-b0fa5ca93599 · outbound

This paper cites Low regularity semi-linear wave equations.

On the optimal Sobolev threshold for evolution equations with rough nonlinearities Low regularity semi-linear wave equations

Reference 58

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T15:34:56.163223Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

source=pdf_text observed=2026-08-07T15:34:55.920778Z digest=sha256:15fa1423d116978429a9f1637f0aabd8af38d3da38ce304f3469f0b655939152

Observation 3442726d-94de-4be3-99c8-6ec4e43236a3 · outbound

This paper cites Global regularity of wave maps.

On the optimal Sobolev threshold for evolution equations with rough nonlinearities Global regularity of wave maps

Reference 59

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T15:34:56.152255Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

source=pdf_text observed=2026-08-07T15:34:55.925810Z digest=sha256:e48d6635cb002c3aa5382f7d40f2269c101d7bdf97fe7fa5f5ec58b29128b1b9

Observation 4a9f6c3b-925a-48fb-9702-faca38850a96 · outbound

This paper cites Global well-posedness and scattering for the hig her-dimensional energy-critical nonlinear Schr¨ odinger equation for radial data.

On the optimal Sobolev threshold for evolution equations with rough nonlinearities Global well-posedness and scattering for the hig her-dimensional energy-critical nonlinear Schr¨ odinger equation for radial data

Reference 60

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T15:34:56.139806Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

source=pdf_text observed=2026-08-07T15:34:55.930530Z digest=sha256:9dff666eaccacbf3c7236d44dbb80d815b6b5e243cc17f474c101ef07fc3d3e5

Observation 378faeaa-5b4d-474c-a40a-1a10985fbf43 · outbound

This paper cites Nonlinear dispersive equations: local and global analysis , volume 106 of CBMS Regional Conference Series in Mathematics.

On the optimal Sobolev threshold for evolution equations with rough nonlinearities Nonlinear dispersive equations: local and global analysis , volume 106 of CBMS Regional Conference Series in Mathematics

Reference 61

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T15:34:56.124672Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

source=pdf_text observed=2026-08-07T15:34:55.934717Z digest=sha256:3eea5c88a742315f2ccb9a796749da33cf8b604c02a98aeb680c7d628baff54c

Observation 08528db2-ee87-455f-8658-ba3ab2db906a · outbound

This paper cites an unresolved cited work.

On the optimal Sobolev threshold for evolution equations with rough nonlinearities Unresolved cited work

Reference 62

Resolution
unresolved
raw_fallback, observed 2026-08-07T15:34:56.111832Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

source=pdf_text observed=2026-08-07T15:34:55.938896Z digest=sha256:dc6fc7474195f9a650c313b47734c97f3d6bb47921bea05b9254bcc70eb0e6ff

Observation 7b5e40e2-0120-486a-8e4f-ac97840151cc · outbound

This paper cites Global strong solutions for nonlinear Schr¨ od inger equations.

On the optimal Sobolev threshold for evolution equations with rough nonlinearities Global strong solutions for nonlinear Schr¨ od inger equations

Reference 63

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T15:34:56.097914Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

source=pdf_text observed=2026-08-07T15:34:55.943625Z digest=sha256:ff072312439284c7834523f3c49cb6f4d76610c31a4a702bd2fd11a47e1061ff

Observation b56869e2-c4c7-4be9-b3b7-f13ba184cff0 · outbound

This paper cites On well-posedness for n onlinear Schr¨ odinger equations with power non- linearity in fractional order Sobolev spaces.

On the optimal Sobolev threshold for evolution equations with rough nonlinearities On well-posedness for n onlinear Schr¨ odinger equations with power non- linearity in fractional order Sobolev spaces

Reference 64

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T15:34:56.085112Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

source=pdf_text observed=2026-08-07T15:34:55.947024Z digest=sha256:b40c46035457d3a61537557c8b6551de6719da1e2c0205202701016d772774f3

Observation b1e6d8be-bb62-4898-84e7-888170ab3ded · outbound

This paper cites The defocusing energy-critical nonlinear Schroedinger eq uation in dimensions five and higher.

On the optimal Sobolev threshold for evolution equations with rough nonlinearities The defocusing energy-critical nonlinear Schroedinger eq uation in dimensions five and higher

Reference 65

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T15:34:56.072555Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

source=pdf_text observed=2026-08-07T15:34:55.950640Z digest=sha256:83628e0bad36c2e65a0b34f8235c02cdb55a3835de5e856546f2594f641628d6

Observation 45a8ac40-573b-4a5b-b64e-3326ace37aa6 · outbound

This paper cites The defocusing energy-critical nonlinear Schr¨ o dinger equation in higher dimensions.

On the optimal Sobolev threshold for evolution equations with rough nonlinearities The defocusing energy-critical nonlinear Schr¨ o dinger equation in higher dimensions

Reference 66

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T15:34:56.060658Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

source=pdf_text observed=2026-08-07T15:34:55.954198Z digest=sha256:3ea2483ffe0e7c0a09f805181c128a1aa09ede4fca835c593ec64eed79386542

Observation f22bd29f-5de3-4aae-aaab-f313af90247e · outbound

This paper cites A remark on local well-posedness for nonlinear S chr¨ odinger equations with power nonlinearity— an alternative approach.

On the optimal Sobolev threshold for evolution equations with rough nonlinearities A remark on local well-posedness for nonlinear S chr¨ odinger equations with power nonlinearity— an alternative approach

Reference 67

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T15:34:56.048405Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

source=pdf_text observed=2026-08-07T15:34:55.958848Z digest=sha256:79de5b7eb0ffe7348f302863bc229ffea4c1107ab4cd6c8077f3de17e4520157

Pith citing papers

No inbound Pith citation observations are available.