Paper Citation Record · LEDGER

Global existence and optimal decay for a three-dimensional penalized Navier--Stokes system with biharmonic damping

As of 11 August 2026, this Paper Citation Record lists 31 of 31 outbound references and 0 inbound Pith citation observations for arXiv:2607.10657.

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

pith.paper-citation-record.v1
2607.10657 v1

Coverage vector

measured 31 of 31 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-07-14T10:10:24.457945Z

measured 31 of 31 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-11T06:34:44.6726+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

31 of 31 outbound references displayed

verified exact0
verified fuzzy0
unresolved31
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation fef2ad34-0738-48b4-9fb0-06c6b3390f55 · outbound

This paper cites an unresolved cited work.

Global existence and optimal decay for a three-dimensional penalized Navier--Stokes system with biharmonic damping Unresolved cited work

Reference 1

Resolution: unresolved; no resolver link, observed 2026-07-14T10:10:24.457945Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 92f4ba9a-ba2d-4770-9043-8ff2e2cacbc9 · outbound

This paper cites Asai and Y.

Global existence and optimal decay for a three-dimensional penalized Navier--Stokes system with biharmonic damping Asai and Y

Reference 2

Resolution: unresolved; no resolver link, observed 2026-07-14T10:10:24.457945Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 1ad3ac18-d9cb-4c7b-9af6-e868fb189ca2 · outbound

This paper cites Caffarelli, R.

Global existence and optimal decay for a three-dimensional penalized Navier--Stokes system with biharmonic damping Caffarelli, R

Reference 3

Resolution: unresolved; no resolver link, observed 2026-07-14T10:10:24.457945Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 1b03cc0d-cc3b-4c76-9464-b247b655dae6 · outbound

This paper cites Cai and Q.S.

Global existence and optimal decay for a three-dimensional penalized Navier--Stokes system with biharmonic damping Cai and Q.S

Reference 4

Resolution: unresolved; no resolver link, observed 2026-07-14T10:10:24.457945Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 95b47291-3bce-4435-9d90-eea51e6dc9c6 · outbound

This paper cites Escudero, F.

Global existence and optimal decay for a three-dimensional penalized Navier--Stokes system with biharmonic damping Escudero, F

Reference 5

Resolution: unresolved; no resolver link, observed 2026-07-14T10:10:24.457945Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation ecb7a910-1a89-4364-88aa-182c86cc6628 · outbound

This paper cites an unresolved cited work.

Global existence and optimal decay for a three-dimensional penalized Navier--Stokes system with biharmonic damping Unresolved cited work

Reference 6

Resolution: unresolved; no resolver link, observed 2026-07-14T10:10:24.457945Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 86271535-2bb6-4f62-a294-4ddd4d4475fb · outbound

This paper cites Hopf,Über die Anfangswertaufgabe für die hydrodynamischen Grundgleichungen, Math.

Global existence and optimal decay for a three-dimensional penalized Navier--Stokes system with biharmonic damping Hopf,Über die Anfangswertaufgabe für die hydrodynamischen Grundgleichungen, Math

Reference 7

Resolution: unresolved; no resolver link, observed 2026-07-14T10:10:24.457945Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 66a771c4-53f9-42db-b8d9-b79deb205111 · outbound

This paper cites Kalantarov and S.

Global existence and optimal decay for a three-dimensional penalized Navier--Stokes system with biharmonic damping Kalantarov and S

Reference 8

Resolution: unresolved; no resolver link, observed 2026-07-14T10:10:24.457945Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation aaa8c402-da17-4627-bf49-efbfde16fa69 · outbound

This paper cites an unresolved cited work.

Global existence and optimal decay for a three-dimensional penalized Navier--Stokes system with biharmonic damping Unresolved cited work

Reference 9

Resolution: unresolved; no resolver link, observed 2026-07-14T10:10:24.457945Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 3c1793d6-2b9c-4858-94b1-4c032ae80c23 · outbound

This paper cites Leray,Sur le mouvement d’un liquide visqueux emplissant l’espace, Acta Math.,63(1934), 193– 248.

Global existence and optimal decay for a three-dimensional penalized Navier--Stokes system with biharmonic damping Leray,Sur le mouvement d’un liquide visqueux emplissant l’espace, Acta Math.,63(1934), 193– 248

Reference 10

Resolution: unresolved; no resolver link, observed 2026-07-14T10:10:24.457945Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation c8268186-e90a-41b9-bb0b-dc21d190e7bc · outbound

This paper cites an unresolved cited work.

Global existence and optimal decay for a three-dimensional penalized Navier--Stokes system with biharmonic damping Unresolved cited work

Reference 11

Resolution: unresolved; no resolver link, observed 2026-07-14T10:10:24.457945Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 763b2e5b-7133-42a8-9367-2e9808d8045e · outbound

This paper cites Lions,Quelques méthodes de résolution des problèmes aux limites non linéaires, Dunod; Gauthier-Villars, Paris, 1969.

Global existence and optimal decay for a three-dimensional penalized Navier--Stokes system with biharmonic damping Lions,Quelques méthodes de résolution des problèmes aux limites non linéaires, Dunod; Gauthier-Villars, Paris, 1969

Reference 12

Resolution: unresolved; no resolver link, observed 2026-07-14T10:10:24.457945Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation a325a03e-0bcc-4e64-9e68-ec4dd7c1ee5b · outbound

This paper cites Pal and R.

Global existence and optimal decay for a three-dimensional penalized Navier--Stokes system with biharmonic damping Pal and R

Reference 13

Resolution: unresolved; no resolver link, observed 2026-07-14T10:10:24.457945Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 54472cb5-0a7b-4836-b6d0-4cf57eb23f29 · outbound

This paper cites Plecháč and V.

Global existence and optimal decay for a three-dimensional penalized Navier--Stokes system with biharmonic damping Plecháč and V

Reference 14

Resolution: unresolved; no resolver link, observed 2026-07-14T10:10:24.457945Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 82089267-c400-45ca-9b98-d775eecce156 · outbound

This paper cites an unresolved cited work.

Global existence and optimal decay for a three-dimensional penalized Navier--Stokes system with biharmonic damping Unresolved cited work

Reference 15

Resolution: unresolved; no resolver link, observed 2026-07-14T10:10:24.457945Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 039350aa-ea81-4192-ab0c-80da4149b6ca · outbound

This paper cites Röckner and X.

Global existence and optimal decay for a three-dimensional penalized Navier--Stokes system with biharmonic damping Röckner and X

Reference 16

Resolution: unresolved; no resolver link, observed 2026-07-14T10:10:24.457945Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 92da4366-c19e-407f-a50c-545639244f32 · outbound

This paper cites an unresolved cited work.

Global existence and optimal decay for a three-dimensional penalized Navier--Stokes system with biharmonic damping Unresolved cited work

Reference 17

Resolution: unresolved; no resolver link, observed 2026-07-14T10:10:24.457945Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 090ab045-6bcc-4630-9683-0bdbc99e3b5b · outbound

This paper cites an unresolved cited work.

Global existence and optimal decay for a three-dimensional penalized Navier--Stokes system with biharmonic damping Unresolved cited work

Reference 18

Resolution: unresolved; no resolver link, observed 2026-07-14T10:10:24.457945Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation dc9b1601-48e1-45f5-a30c-bb06c0e72ca4 · outbound

This paper cites Shen,On error estimates of the penalty method for unsteady Navier–Stokes equations, SIAM J.

Global existence and optimal decay for a three-dimensional penalized Navier--Stokes system with biharmonic damping Shen,On error estimates of the penalty method for unsteady Navier–Stokes equations, SIAM J

Reference 19

Resolution: unresolved; no resolver link, observed 2026-07-14T10:10:24.457945Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation ff34f0a8-a0e1-4939-878c-696318a8356c · outbound

This paper cites Struwe,On partial regularity results for the Navier–Stokes equations, Comm.

Global existence and optimal decay for a three-dimensional penalized Navier--Stokes system with biharmonic damping Struwe,On partial regularity results for the Navier–Stokes equations, Comm

Reference 20

Resolution: unresolved; no resolver link, observed 2026-07-14T10:10:24.457945Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 36e0303d-cf02-4ee0-abbd-d381e5325c7d · outbound

This paper cites an unresolved cited work.

Global existence and optimal decay for a three-dimensional penalized Navier--Stokes system with biharmonic damping Unresolved cited work

Reference 21

Resolution: unresolved; no resolver link, observed 2026-07-14T10:10:24.457945Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 8f7c92f9-f936-4448-8a1a-7511b2f46b2d · outbound

This paper cites Tao,Global regularity for a logarithmically supercritical hyperdissipative Navier–Stokes equation, Anal.

Global existence and optimal decay for a three-dimensional penalized Navier--Stokes system with biharmonic damping Tao,Global regularity for a logarithmically supercritical hyperdissipative Navier–Stokes equation, Anal

Reference 22

Resolution: unresolved; no resolver link, observed 2026-07-14T10:10:24.457945Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 630ddce9-d5f1-43d3-88a7-ae68ec3a4956 · outbound

This paper cites Temam,Une méthode d’approximation de la solution des équations de Navier–Stokes, Bull.

Global existence and optimal decay for a three-dimensional penalized Navier--Stokes system with biharmonic damping Temam,Une méthode d’approximation de la solution des équations de Navier–Stokes, Bull

Reference 23

Resolution: unresolved; no resolver link, observed 2026-07-14T10:10:24.457945Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation eff2adfb-df98-4336-beef-7d468059f228 · outbound

This paper cites Temam,Navier–Stokes Equations: Theory and Numerical Analysis, North-Holland, New York, 1984.

Global existence and optimal decay for a three-dimensional penalized Navier--Stokes system with biharmonic damping Temam,Navier–Stokes Equations: Theory and Numerical Analysis, North-Holland, New York, 1984

Reference 24

Resolution: unresolved; no resolver link, observed 2026-07-14T10:10:24.457945Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 58622fec-7f31-4d53-8147-c15988cf2d2a · outbound

This paper cites Vertman,The biharmonic heat operator on edge manifolds and non-linear fourth order equations, Manuscripta Math.,149(2016), 179–203.

Global existence and optimal decay for a three-dimensional penalized Navier--Stokes system with biharmonic damping Vertman,The biharmonic heat operator on edge manifolds and non-linear fourth order equations, Manuscripta Math.,149(2016), 179–203

Reference 25

Resolution: unresolved; no resolver link, observed 2026-07-14T10:10:24.457945Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 6c68ea2e-ccfc-449f-8608-14b1acfa2b99 · outbound

This paper cites Wiegner,Decay results for weak solutions of the Navier–Stokes equations onRn, J.

Global existence and optimal decay for a three-dimensional penalized Navier--Stokes system with biharmonic damping Wiegner,Decay results for weak solutions of the Navier–Stokes equations onRn, J

Reference 26

Resolution: unresolved; no resolver link, observed 2026-07-14T10:10:24.457945Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation e5bd596f-ad5a-4492-ab2a-6dc21b72c394 · outbound

This paper cites Xu and J.

Global existence and optimal decay for a three-dimensional penalized Navier--Stokes system with biharmonic damping Xu and J

Reference 27

Resolution: unresolved; no resolver link, observed 2026-07-14T10:10:24.457945Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation a4031191-0ac8-4bcb-8c21-8a55cba53c2b · outbound

This paper cites an unresolved cited work.

Global existence and optimal decay for a three-dimensional penalized Navier--Stokes system with biharmonic damping Unresolved cited work

Reference 28

Resolution: unresolved; no resolver link, observed 2026-07-14T10:10:24.457945Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation ec993c29-7046-4dde-9bdb-18d606319965 · outbound

This paper cites Zhang, X.

Global existence and optimal decay for a three-dimensional penalized Navier--Stokes system with biharmonic damping Zhang, X

Reference 29

Resolution: unresolved; no resolver link, observed 2026-07-14T10:10:24.457945Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 6f4ac988-a976-4a3a-a04d-b8cd7f802231 · outbound

This paper cites Zhou,Regularity and uniqueness for the 3D incompressible Navier–Stokes equations with damp- ing, Appl.

Global existence and optimal decay for a three-dimensional penalized Navier--Stokes system with biharmonic damping Zhou,Regularity and uniqueness for the 3D incompressible Navier–Stokes equations with damp- ing, Appl

Reference 30

Resolution: unresolved; no resolver link, observed 2026-07-14T10:10:24.457945Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation cad77dbd-c233-4e5f-a5fc-e804dc596ec1 · outbound

This paper cites Zhou and Y.

Global existence and optimal decay for a three-dimensional penalized Navier--Stokes system with biharmonic damping Zhou and Y

Reference 31

Resolution: unresolved; no resolver link, observed 2026-07-14T10:10:24.457945Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Pith citing papers

No inbound Pith citation observations are available.