Paper Citation Record · LEDGER

Scaling-Critical Theory for the Boltzmann and Landau Equations

As of 16 August 2026, this Paper Citation Record lists 89 of 89 outbound references and 2 inbound Pith citation observations for arXiv:2509.14845.

A citation records a reference. It does not transfer a finding from one paper to another.

pith.paper-citation-record.v1
2509.14845 v2

Coverage vector

measured 89 of 89 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-04T16:17:39.012361Z

measured 91 of 91 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-15T06:32:42.880941+00:00

measured 2 of 2 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-02T22:53:07.235085Z

measured 0 of 1 external citation measurements

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

Source: arxiv_reference, observed 2026-05-11T08:56:02.343847Z

Reference resolution

89 of 89 outbound references displayed

verified exact6
verified fuzzy0
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External citation measurements

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Outbound references

Observation 56906f37-d7a6-49fa-9335-778a9285cc45 · outbound

This paper cites Rational Mech.

Scaling-Critical Theory for the Boltzmann and Landau Equations Rational Mech

Reference 1

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Observation 38cc8300-e0e9-46cb-9b0b-701ff1b885ee · outbound

This paper cites Rational Mech.

Scaling-Critical Theory for the Boltzmann and Landau Equations Rational Mech

Reference 2

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Observation 3a7745ad-9734-459a-b6f8-cdb6d4023a7c · outbound

This paper cites and Morimoto, Y.

Scaling-Critical Theory for the Boltzmann and Landau Equations and Morimoto, Y

Reference 3

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Observation 4e3833c8-2765-4b2c-99aa-280426ff52f7 · outbound

This paper cites and Morimoto, Y.

Scaling-Critical Theory for the Boltzmann and Landau Equations and Morimoto, Y

Reference 4

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Observation 80eb548d-260a-4845-9681-f654d970a288 · outbound

This paper cites and Morimoto, Y.

Scaling-Critical Theory for the Boltzmann and Landau Equations and Morimoto, Y

Reference 5

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Scaling-Critical Theory for the Boltzmann and Landau Equations Unresolved cited work

Reference 6

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Observation 00ead511-39f9-41a5-af23-25a2bb7ddc19 · outbound

This paper cites and Villani, C.,On the Landau approximation in plasma physics.Annales de l’Institut Henri Poincar´ e C, Analyse non lin´ eaire, 21(1): 61-95, 2004.

Scaling-Critical Theory for the Boltzmann and Landau Equations and Villani, C.,On the Landau approximation in plasma physics.Annales de l’Institut Henri Poincar´ e C, Analyse non lin´ eaire, 21(1): 61-95, 2004

Reference 7

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Observation afc3f152-77c5-41dc-a76b-7db07f744de2 · outbound

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Scaling-Critical Theory for the Boltzmann and Landau Equations Unresolved cited work

Reference 8

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Observation 4b7bf53b-5d94-4465-9922-05c72b86000b · outbound

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Scaling-Critical Theory for the Boltzmann and Landau Equations Unresolved cited work

Reference 9

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Observation 6892dcbd-fc31-4e9d-bfa9-41cd50bff15d · outbound

This paper cites Arch Rational Mech Anal 248, 42 (2024).

Scaling-Critical Theory for the Boltzmann and Landau Equations Arch Rational Mech Anal 248, 42 (2024)

Reference 10

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Observation 426ac4e0-72cd-42f1-a1d1-d6c8b5e69083 · outbound

This paper cites Pure Appl.

Scaling-Critical Theory for the Boltzmann and Landau Equations Pure Appl

Reference 11

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Scaling-Critical Theory for the Boltzmann and Landau Equations Unresolved cited work

Reference 12

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Observation 39e608f9-e2e0-44b3-8e9b-4316b5a684b0 · outbound

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Scaling-Critical Theory for the Boltzmann and Landau Equations Unresolved cited work

Reference 13

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Observation ca5fabfd-ddf6-4a87-91dd-8d8522b75e28 · outbound

This paper cites , and Pavlovi´ c N.,Ill-posedness of the Navier-Stokes equations in a critical space in 3D.J.

Scaling-Critical Theory for the Boltzmann and Landau Equations , and Pavlovi´ c N.,Ill-posedness of the Navier-Stokes equations in a critical space in 3D.J

Reference 14

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Observation 1dcce04f-1a8e-40c3-a494-db351aae104f · outbound

This paper cites E.,The fluid dynamical limit of the nonlinear Boltzmann equation.Comm.

Scaling-Critical Theory for the Boltzmann and Landau Equations E.,The fluid dynamical limit of the nonlinear Boltzmann equation.Comm

Reference 15

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Scaling-Critical Theory for the Boltzmann and Landau Equations Unresolved cited work

Reference 16

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Observation ee523e14-c5ec-470e-8017-498daca1ce7d · outbound

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Scaling-Critical Theory for the Boltzmann and Landau Equations Unresolved cited work

Reference 17

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Observation b98fac93-3993-47fc-b289-f35e1ab31583 · outbound

This paper cites Annals of PDE, 3, 1-65, (2017).

Scaling-Critical Theory for the Boltzmann and Landau Equations Annals of PDE, 3, 1-65, (2017)

Reference 18

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Observation a3458a16-9982-405a-96f8-340403343d17 · outbound

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Scaling-Critical Theory for the Boltzmann and Landau Equations Unresolved cited work

Reference 19

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Observation 29531aa9-dbd2-41ed-b009-a046ea9e71c9 · outbound

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Scaling-Critical Theory for the Boltzmann and Landau Equations Unresolved cited work

Reference 20

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Observation d17c3e76-0d95-48c3-baf4-e2b37c4e5589 · outbound

This paper cites PDE 7, 15 (2021).

Scaling-Critical Theory for the Boltzmann and Landau Equations PDE 7, 15 (2021)

Reference 21

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Observation 3dc39c82-8068-4e7e-950c-de6b34f3fb1a · outbound

This paper cites L., Li, W.-X.,and Xu, C.J.,Sharp regularization effect for the non-cutoff Boltzmann equation with hard potentials.Ann.

Scaling-Critical Theory for the Boltzmann and Landau Equations L., Li, W.-X.,and Xu, C.J.,Sharp regularization effect for the non-cutoff Boltzmann equation with hard potentials.Ann

Reference 22

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Observation abde8b8d-e519-483f-8451-4ffc5c73440d · outbound

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Scaling-Critical Theory for the Boltzmann and Landau Equations Unresolved cited work

Reference 23

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Observation 00323e9d-4618-4460-84be-6a5c6ae05085 · outbound

This paper cites Well-posedness for local and nonlocal quasilinear evolution equations in fluids and geometry.

Scaling-Critical Theory for the Boltzmann and Landau Equations Well-posedness for local and nonlocal quasilinear evolution equations in fluids and geometry

Reference 24

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Scaling-Critical Theory for the Boltzmann and Landau Equations Unresolved cited work

Reference 25

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Observation e771be2a-3866-489d-aa22-9106eb9d0fd6 · outbound

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Scaling-Critical Theory for the Boltzmann and Landau Equations Unresolved cited work

Reference 26

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Observation b6191842-b180-4d7f-b67a-a6132168c5fa · outbound

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Scaling-Critical Theory for the Boltzmann and Landau Equations Unresolved cited work

Reference 27

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Observation 85f79300-d64c-45b0-9de1-3bac2796cf6c · outbound

This paper cites To appear in Proceedings of the American Mathematical Society.

Scaling-Critical Theory for the Boltzmann and Landau Equations To appear in Proceedings of the American Mathematical Society

Reference 28

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Observation d7284f44-4f93-4d4f-b7e4-9a5a1d785be6 · outbound

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Scaling-Critical Theory for the Boltzmann and Landau Equations Unresolved cited work

Reference 29

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Scaling-Critical Theory for the Boltzmann and Landau Equations Unresolved cited work

Reference 30

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Scaling-Critical Theory for the Boltzmann and Landau Equations Unresolved cited work

Reference 31

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Observation 26d502c2-8db5-49c1-9fae-0d1846503a6d · outbound

This paper cites Sharp Global Well-posedness and Scattering of the Boltzmann Equation.

Scaling-Critical Theory for the Boltzmann and Landau Equations Sharp Global Well-posedness and Scattering of the Boltzmann Equation

Reference 32

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Scaling-Critical Theory for the Boltzmann and Landau Equations Unresolved cited work

Reference 33

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Observation 4e7c89d6-aba3-4c0f-88fd-3ed75cefd5ab · outbound

This paper cites and Villani, C.,On the spatially homogeneous Landau equation for hard potentials.

Scaling-Critical Theory for the Boltzmann and Landau Equations and Villani, C.,On the spatially homogeneous Landau equation for hard potentials

Reference 34

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Observation 9ccabfbf-1d28-4200-85e7-3cc81bd3cb3b · outbound

This paper cites Communications in Partial Differential Equations, 25(1-2), 261-298, (2000).

Scaling-Critical Theory for the Boltzmann and Landau Equations Communications in Partial Differential Equations, 25(1-2), 261-298, (2000)

Reference 35

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Observation 723d1d5e-d57e-465f-99d4-4230ed6ad701 · outbound

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Scaling-Critical Theory for the Boltzmann and Landau Equations Unresolved cited work

Reference 36

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Observation 6959d6bd-4bda-42c2-9803-9d266853f836 · outbound

This paper cites and Liu S.-Q.,The Boltzmann equation for uniform shear flow.Arch.

Scaling-Critical Theory for the Boltzmann and Landau Equations and Liu S.-Q.,The Boltzmann equation for uniform shear flow.Arch

Reference 37

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Observation 88ac0fbb-f322-4db9-8785-c4063fc5b3ad · outbound

This paper cites Arch Rational Mech Anal 199, 291–328 (2011).

Scaling-Critical Theory for the Boltzmann and Landau Equations Arch Rational Mech Anal 199, 291–328 (2011)

Reference 38

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Observation daa6cb81-e5f5-493d-a4d8-1560a04c2973 · outbound

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Scaling-Critical Theory for the Boltzmann and Landau Equations Unresolved cited work

Reference 39

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Scaling-Critical Theory for the Boltzmann and Landau Equations Unresolved cited work

Reference 40

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This paper cites M.,Global mild solutions of the Landau and non-cutoff Boltzmann equations,Comm.

Scaling-Critical Theory for the Boltzmann and Landau Equations M.,Global mild solutions of the Landau and non-cutoff Boltzmann equations,Comm

Reference 41

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Scaling-Critical Theory for the Boltzmann and Landau Equations Unresolved cited work

Reference 42

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Observation 2799f65c-dc8d-4a42-b4ea-9d8e3f6943b0 · outbound

This paper cites https://doi.org/10.1007/s00205-023-01901-9 55.

Scaling-Critical Theory for the Boltzmann and Landau Equations https://doi.org/10.1007/s00205-023-01901-9 55

Reference 43

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Observation a3460341-5acb-4875-b1e9-8f73d6f44f2e · outbound

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Scaling-Critical Theory for the Boltzmann and Landau Equations Unresolved cited work

Reference 44

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Scaling-Critical Theory for the Boltzmann and Landau Equations Unresolved cited work

Reference 45

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Scaling-Critical Theory for the Boltzmann and Landau Equations Unresolved cited work

Reference 46

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Scaling-Critical Theory for the Boltzmann and Landau Equations Unresolved cited work

Reference 47

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Observation 94a426be-53eb-49d8-afa5-d3389feddfaf · outbound

This paper cites F.,Local regularity for the space-homogenous Landau equation with very soft potentials.J.

Scaling-Critical Theory for the Boltzmann and Landau Equations F.,Local regularity for the space-homogenous Landau equation with very soft potentials.J

Reference 48

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Observation 7b25c9e1-4b7a-48fc-af10-774a78207948 · outbound

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Scaling-Critical Theory for the Boltzmann and Landau Equations Classical Fourier Analysis

Reference 49

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Scaling-Critical Theory for the Boltzmann and Landau Equations Unresolved cited work

Reference 50

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This paper cites Grube,Pointwise estimates of the fundamental solution to the fractional Kolmogorov equation,arXiv:.

Scaling-Critical Theory for the Boltzmann and Landau Equations Grube,Pointwise estimates of the fundamental solution to the fractional Kolmogorov equation,arXiv:

Reference 51

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Scaling-Critical Theory for the Boltzmann and Landau Equations Unresolved cited work

Reference 52

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Scaling-Critical Theory for the Boltzmann and Landau Equations Unresolved cited work

Reference 53

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Scaling-Critical Theory for the Boltzmann and Landau Equations Unresolved cited work

Reference 54

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Scaling-Critical Theory for the Boltzmann and Landau Equations Pure Appl

Reference 55

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Scaling-Critical Theory for the Boltzmann and Landau Equations Unresolved cited work

Reference 56

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Scaling-Critical Theory for the Boltzmann and Landau Equations Unresolved cited work

Reference 57

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This paper cites Annales de l’Institut Henri Poincar´ e C, Analyse non lin´ eaire.

Scaling-Critical Theory for the Boltzmann and Landau Equations Annales de l’Institut Henri Poincar´ e C, Analyse non lin´ eaire

Reference 58

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Scaling-Critical Theory for the Boltzmann and Landau Equations Classical solutions of the Boltzmann equation with irregular initial data

Reference 59

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Scaling-Critical Theory for the Boltzmann and Landau Equations Unresolved cited work

Reference 60

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This paper cites Quarterly of applied mathematics, 65(2), 281–315, (2007).

Scaling-Critical Theory for the Boltzmann and Landau Equations Quarterly of applied mathematics, 65(2), 281–315, (2007)

Reference 61

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Scaling-Critical Theory for the Boltzmann and Landau Equations Unresolved cited work

Reference 62

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This paper cites arXiv: 2410.18164.

Scaling-Critical Theory for the Boltzmann and Landau Equations arXiv: 2410.18164

Reference 63

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Reference 65

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Reference 67

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Reference 68

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Reference 69

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Scaling-Critical Theory for the Boltzmann and Landau Equations N.Effective interactions in soft condensed matter physics.Physics Reports, 348(4-5), 267–439, (2001)

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Reference 71

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Reference 73

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Reference 74

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Reference 75

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Reference 76

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Reference 77

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Observation cf155173-e162-4b37-94b0-7159517260db · outbound

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Observation 4c7be50d-445e-43ec-9ad5-e7ed78145110 · outbound

This paper cites an unresolved cited work.

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Reference 79

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Reference 80

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Reference 81

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Reference 82

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Reference 83

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Reference 84

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Observation 9ee35763-7677-4376-b118-588fb8a99071 · outbound

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Scaling-Critical Theory for the Boltzmann and Landau Equations 273–307, (1998)

Reference 86

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Reference 87

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Scaling-Critical Theory for the Boltzmann and Landau Equations Handbook of mathematical fluid dynamics, 1(71-305):3–8, 2002

Reference 88

Resolution: unresolved; no resolver link, observed 2026-08-04T16:17:38.835512Z

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Observation b3ffab21-30c4-4998-a71d-224947f5680b · outbound

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Reference 89

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Pith citing papers

Observation dd9bb7c3-fb40-4ba6-8106-7247990ff2af · inbound

Uniqueness and Zeroth-Order Analysis of Weak Solutions to the Non-cutoff Boltzmann equation cites this paper.

Uniqueness and Zeroth-Order Analysis of Weak Solutions to the Non-cutoff Boltzmann equation Scaling-Critical Theory for the Boltzmann and Landau Equations

Reference 17

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Observation 8bb80524-4c87-44da-8e30-845b26e980fd · inbound

Schauder-type Estimates and Well-posedness for Nonlocal Quasilinear Evolution Equations in Fluid Dynamics cites this paper.

Schauder-type Estimates and Well-posedness for Nonlocal Quasilinear Evolution Equations in Fluid Dynamics Scaling-Critical Theory for the Boltzmann and Landau Equations

Reference 28

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