Paper Citation Record · LEDGER

Sharp non-uniqueness for the Navier-Stokes equations in scaling critical spaces

As of 8 August 2026, this Paper Citation Record lists 63 of 63 outbound references and 2 inbound Pith citation observations for arXiv:2602.19846.

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

pith.paper-citation-record.v1
2602.19846 v4

Coverage vector

measured 63 of 63 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-02T21:43:27.182728Z

measured 65 of 65 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-08T06:32:00.761636+00:00

measured 2 of 2 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-02T19:14:29.482666Z

measured 0 of 1 external citation measurements

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

Source: pith, observed 2026-07-03T15:58:38.280603Z

Reference resolution

63 of 63 outbound references displayed

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External citation measurements

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Outbound references

Observation d13cb8b2-e456-499c-9faf-0f60e820703a · outbound

This paper cites Abidi and M.

Sharp non-uniqueness for the Navier-Stokes equations in scaling critical spaces Abidi and M

Reference 1

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Observation b5a3fe9b-3d17-46c0-82a2-525945005f72 · outbound

This paper cites Albritton, E.

Sharp non-uniqueness for the Navier-Stokes equations in scaling critical spaces Albritton, E

Reference 2

Resolution: unresolved; no resolver link, observed 2026-08-02T21:43:21.795608Z

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Observation b7de97eb-2dac-494b-93bf-2324cd485acc · outbound

This paper cites Self-similar vorticity around the boundary and non-uniqueness of solutions to the two-dimensional Navier-Stokes equations in the half space.

Sharp non-uniqueness for the Navier-Stokes equations in scaling critical spaces Self-similar vorticity around the boundary and non-uniqueness of solutions to the two-dimensional Navier-Stokes equations in the half space

Reference 3

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Observation c9381321-f877-4bd0-8c9c-68add148492d · outbound

This paper cites Bahouri, J.-Y.

Sharp non-uniqueness for the Navier-Stokes equations in scaling critical spaces Bahouri, J.-Y

Reference 4

Resolution: unresolved; no resolver link, observed 2026-08-02T21:43:21.942673Z

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Observation 307229ea-eed8-4e1b-a033-31394cab039c · outbound

This paper cites Benameur,Long time decay to the Lei-Lin solution of 3D Navier-Stokes equations, J.

Sharp non-uniqueness for the Navier-Stokes equations in scaling critical spaces Benameur,Long time decay to the Lei-Lin solution of 3D Navier-Stokes equations, J

Reference 5

Resolution: unresolved; no resolver link, observed 2026-08-02T21:43:22.108156Z

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Observation bf25874d-3e4e-4c69-aa73-6bcac8550b17 · outbound

This paper cites Bourgain and N.

Sharp non-uniqueness for the Navier-Stokes equations in scaling critical spaces Bourgain and N

Reference 6

Resolution: unresolved; no resolver link, observed 2026-08-02T21:43:22.201406Z

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Observation daf2958f-d1fd-459d-92f8-a0ab184c1957 · outbound

This paper cites Buckmaster, C.

Sharp non-uniqueness for the Navier-Stokes equations in scaling critical spaces Buckmaster, C

Reference 7

Resolution: unresolved; no resolver link, observed 2026-08-02T21:43:22.342729Z

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Observation 7cf20d61-4c74-4bd2-8257-0dbcddedb5e5 · outbound

This paper cites Buckmaster and V.

Sharp non-uniqueness for the Navier-Stokes equations in scaling critical spaces Buckmaster and V

Reference 8

Resolution: unresolved; no resolver link, observed 2026-08-02T21:43:22.427026Z

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Observation 8a750105-0acc-4f16-8d83-33e8bdc619f5 · outbound

This paper cites Cannone and F.

Sharp non-uniqueness for the Navier-Stokes equations in scaling critical spaces Cannone and F

Reference 9

Resolution: unresolved; no resolver link, observed 2026-08-02T21:43:22.543926Z

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Observation 36f34166-894a-4d90-b982-0fcdd88db638 · outbound

This paper cites Chemin,Remarques sur l’existence globale pour le système de Navier-Stokes incom- pressible, SIAM J.

Sharp non-uniqueness for the Navier-Stokes equations in scaling critical spaces Chemin,Remarques sur l’existence globale pour le système de Navier-Stokes incom- pressible, SIAM J

Reference 10

Resolution: unresolved; no resolver link, observed 2026-08-02T21:43:22.632881Z

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Observation 24da652f-dc01-49f9-8055-657ead618b78 · outbound

This paper cites Chemin and N.

Sharp non-uniqueness for the Navier-Stokes equations in scaling critical spaces Chemin and N

Reference 11

Resolution: unresolved; no resolver link, observed 2026-08-02T21:43:22.728793Z

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Observation db55ab54-172c-4121-8dcf-540b890f7a0c · outbound

This paper cites an unresolved cited work.

Sharp non-uniqueness for the Navier-Stokes equations in scaling critical spaces Unresolved cited work

Reference 12

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Observation fdd58ab6-a73e-4ac0-8ef8-6f63b1b9695e · outbound

This paper cites Cheskidov and X.

Sharp non-uniqueness for the Navier-Stokes equations in scaling critical spaces Cheskidov and X

Reference 13

Resolution: unresolved; no resolver link, observed 2026-08-02T21:43:22.842791Z

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Observation 3ca87f43-c5f3-4820-9135-900cd0dde453 · outbound

This paper cites PDE9(2023), Paper No.

Sharp non-uniqueness for the Navier-Stokes equations in scaling critical spaces PDE9(2023), Paper No

Reference 14

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Observation 07d1f737-061c-4e2c-9384-656aaa54c7c0 · outbound

This paper cites Global dissipative solutions of the 3D Naiver-Stokes and MHD equations.

Sharp non-uniqueness for the Navier-Stokes equations in scaling critical spaces Global dissipative solutions of the 3D Naiver-Stokes and MHD equations

Reference 15

Resolution: unresolved; no resolver link, observed 2026-08-02T21:43:23.067046Z

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Observation 556cda0f-9517-48b4-9e75-45d8ced5efcf · outbound

This paper cites Cheskidov, M.

Sharp non-uniqueness for the Navier-Stokes equations in scaling critical spaces Cheskidov, M

Reference 16

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Observation 8edf71c1-8b10-4102-93f8-e70c7e8cddd7 · outbound

This paper cites an unresolved cited work.

Sharp non-uniqueness for the Navier-Stokes equations in scaling critical spaces Unresolved cited work

Reference 17

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Observation 732477b5-f05e-47fe-9a8e-b3a72b93df80 · outbound

This paper cites Daneri and L.

Sharp non-uniqueness for the Navier-Stokes equations in scaling critical spaces Daneri and L

Reference 18

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Observation 3db891a6-c14d-46ed-8a1a-85f772618432 · outbound

This paper cites De Lellis and L.

Sharp non-uniqueness for the Navier-Stokes equations in scaling critical spaces De Lellis and L

Reference 19

Resolution: unresolved; no resolver link, observed 2026-08-02T21:43:23.418222Z

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Observation 96c33626-be12-4f66-954f-2c8ce2088e26 · outbound

This paper cites Math.193(2013), 377–407.

Sharp non-uniqueness for the Navier-Stokes equations in scaling critical spaces Math.193(2013), 377–407

Reference 20

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Observation 869d49ea-1a93-4623-a1ce-e05e646496ab · outbound

This paper cites Eskauriaza, G.

Sharp non-uniqueness for the Navier-Stokes equations in scaling critical spaces Eskauriaza, G

Reference 21

Resolution: unresolved; no resolver link, observed 2026-08-02T21:43:23.555769Z

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Observation c7398fbe-16f5-4bef-80e7-d84d66e9fb3d · outbound

This paper cites Fujii,Ill-Posedness of the Two-Dimensional Stationary Navier–Stokes Equations on the Whole Plane, Ann.

Sharp non-uniqueness for the Navier-Stokes equations in scaling critical spaces Fujii,Ill-Posedness of the Two-Dimensional Stationary Navier–Stokes Equations on the Whole Plane, Ann

Reference 22

Resolution: unresolved; no resolver link, observed 2026-08-02T21:43:23.607373Z

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Observation cdba62d0-ddb2-40d4-8279-380346497640 · outbound

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Sharp non-uniqueness for the Navier-Stokes equations in scaling critical spaces Unresolved cited work

Reference 23

Resolution: unresolved; no resolver link, observed 2026-08-02T21:43:23.686304Z

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Observation 1b817f27-d7e3-4867-9475-036af75e41d1 · outbound

This paper cites Fujii and H.

Sharp non-uniqueness for the Navier-Stokes equations in scaling critical spaces Fujii and H

Reference 24

Resolution: unresolved; no resolver link, observed 2026-08-02T21:43:23.782868Z

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Observation 74f2ea84-5f67-4b5a-abdb-fc0b4e12c02e · outbound

This paper cites Fujita and T.

Sharp non-uniqueness for the Navier-Stokes equations in scaling critical spaces Fujita and T

Reference 25

Resolution: unresolved; no resolver link, observed 2026-08-02T21:43:23.835942Z

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Observation dc63ce20-7c82-4e99-96be-346991ada4d6 · outbound

This paper cites Furioli, P.

Sharp non-uniqueness for the Navier-Stokes equations in scaling critical spaces Furioli, P

Reference 26

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Observation 85cdf6ef-1844-4d49-bcea-7ce5046d8f65 · outbound

This paper cites Équations aux Dérivées Partielles.

Sharp non-uniqueness for the Navier-Stokes equations in scaling critical spaces Équations aux Dérivées Partielles

Reference 27

Resolution: unresolved; no resolver link, observed 2026-08-02T21:43:23.951460Z

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Observation 82ce6c6e-4dc3-4488-85b1-e7ea36e1897b · outbound

This paper cites Gallagher, D.

Sharp non-uniqueness for the Navier-Stokes equations in scaling critical spaces Gallagher, D

Reference 28

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Observation bdc84ea9-2bb5-4b77-ba58-3bcbc768c299 · outbound

This paper cites Giga and T.

Sharp non-uniqueness for the Navier-Stokes equations in scaling critical spaces Giga and T

Reference 29

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Observation cdec3f5c-7dd2-4d3e-994e-ae3f3410c828 · outbound

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Sharp non-uniqueness for the Navier-Stokes equations in scaling critical spaces Unresolved cited work

Reference 30

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Observation 41aabc4b-0c36-4d70-af99-cba804c38006 · outbound

This paper cites Isett,A proof of Onsager’s conjecture, Ann.

Sharp non-uniqueness for the Navier-Stokes equations in scaling critical spaces Isett,A proof of Onsager’s conjecture, Ann

Reference 31

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Observation 11999a10-4ba7-4b67-ba05-1ee7f94684aa · outbound

This paper cites Iwabuchi and M.

Sharp non-uniqueness for the Navier-Stokes equations in scaling critical spaces Iwabuchi and M

Reference 32

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Observation 366cc48a-3dfb-4fdb-8de1-2723799ea124 · outbound

This paper cites Iwabuchi and T.

Sharp non-uniqueness for the Navier-Stokes equations in scaling critical spaces Iwabuchi and T

Reference 33

Resolution: unresolved; no resolver link, observed 2026-08-02T21:43:24.357653Z

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Observation ee8c78bd-1d0c-4ef4-b982-2f594492f5db · outbound

This paper cites Jia and V.

Sharp non-uniqueness for the Navier-Stokes equations in scaling critical spaces Jia and V

Reference 34

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Observation c86e3961-bef2-41dd-9cfb-efecfc55345c · outbound

This paper cites Jia and V.

Sharp non-uniqueness for the Navier-Stokes equations in scaling critical spaces Jia and V

Reference 35

Resolution: unresolved; no resolver link, observed 2026-08-02T21:43:24.472861Z

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Observation e8f225a6-d049-4c2d-b746-27f3ba9e6749 · outbound

This paper cites Kaneko, H.

Sharp non-uniqueness for the Navier-Stokes equations in scaling critical spaces Kaneko, H

Reference 36

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Observation 04ffcaa1-1415-4ccb-b79a-c09f19dfa5a3 · outbound

This paper cites Kato,StrongL p-solutions of the Navier-Stokes equation inRm, with applications to weak solutions, Math.

Sharp non-uniqueness for the Navier-Stokes equations in scaling critical spaces Kato,StrongL p-solutions of the Navier-Stokes equation inRm, with applications to weak solutions, Math

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Observation 4c6898c9-4752-44cb-8e82-12d7a3a0f69c · outbound

This paper cites Koch and D.

Sharp non-uniqueness for the Navier-Stokes equations in scaling critical spaces Koch and D

Reference 38

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Observation 166fd81e-237a-47e5-b034-ef97b3e1ed89 · outbound

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Sharp non-uniqueness for the Navier-Stokes equations in scaling critical spaces Kozono and S

Reference 39

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Observation c22bfc00-33f3-460e-a479-c4654ea429b6 · outbound

This paper cites Kozono and H.

Sharp non-uniqueness for the Navier-Stokes equations in scaling critical spaces Kozono and H

Reference 40

Resolution: unresolved; no resolver link, observed 2026-08-02T21:43:24.979915Z

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Observation faa9403c-a0ab-4018-a6a0-51317843c0a0 · outbound

This paper cites Kozono and M.

Sharp non-uniqueness for the Navier-Stokes equations in scaling critical spaces Kozono and M

Reference 41

Resolution: unresolved; no resolver link, observed 2026-08-02T21:43:25.078209Z

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Observation 44b03977-c52c-4dba-a090-da5baaa8a914 · outbound

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Sharp non-uniqueness for the Navier-Stokes equations in scaling critical spaces Unresolved cited work

Reference 42

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Observation 6cc4f166-3c1f-4bc0-8545-5a7764b600a7 · outbound

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

Sharp non-uniqueness for the Navier-Stokes equations in scaling critical spaces Leray,Sur le mouvement d’un liquide visqueux emplissant l’espace, Acta Math.63(1934), 193–248 (French)

Reference 43

Resolution: unresolved; no resolver link, observed 2026-08-02T21:43:25.319663Z

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Observation a36a11ad-a0b9-4349-8267-103fb7caf2e6 · outbound

This paper cites an unresolved cited work.

Sharp non-uniqueness for the Navier-Stokes equations in scaling critical spaces Unresolved cited work

Reference 44

Resolution: unresolved; no resolver link, observed 2026-08-02T21:43:25.437025Z

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Observation c9226179-87bc-4df6-b425-0a0f9c5ec4fc · outbound

This paper cites Lions and N.

Sharp non-uniqueness for the Navier-Stokes equations in scaling critical spaces Lions and N

Reference 45

Resolution: unresolved; no resolver link, observed 2026-08-02T21:43:25.519694Z

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Observation 0b969853-206b-4ee3-a382-5e111cfe5c87 · outbound

This paper cites Luo,Stationary solutions and nonuniqueness of weak solutions for the Navier-Stokes equa- tions in high dimensions, Arch.

Sharp non-uniqueness for the Navier-Stokes equations in scaling critical spaces Luo,Stationary solutions and nonuniqueness of weak solutions for the Navier-Stokes equa- tions in high dimensions, Arch

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Resolution: unresolved; no resolver link, observed 2026-08-02T21:43:25.673872Z

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Observation 40a091c3-543f-4717-996a-5af8eda07331 · outbound

This paper cites Masuda,Weak solutions of Navier-Stokes equations, Tohoku Math.

Sharp non-uniqueness for the Navier-Stokes equations in scaling critical spaces Masuda,Weak solutions of Navier-Stokes equations, Tohoku Math

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Resolution: unresolved; no resolver link, observed 2026-08-02T21:43:25.779858Z

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Observation ef21df1c-f509-4a91-934a-894dca3c50f6 · outbound

This paper cites Miura,Remark on uniqueness of mild solutions to the Navier-Stokes equations, J.

Sharp non-uniqueness for the Navier-Stokes equations in scaling critical spaces Miura,Remark on uniqueness of mild solutions to the Navier-Stokes equations, J

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Resolution: unresolved; no resolver link, observed 2026-08-02T21:43:25.829165Z

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Observation 8ce7e4d3-38c6-428a-9b1b-96d3a1ab4f4c · outbound

This paper cites Nakasato,Analyticity and asymptotic behavior of solutions to the Navier-Stokes equations in an end-point scaling critical framework, J.

Sharp non-uniqueness for the Navier-Stokes equations in scaling critical spaces Nakasato,Analyticity and asymptotic behavior of solutions to the Navier-Stokes equations in an end-point scaling critical framework, J

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Resolution: unresolved; no resolver link, observed 2026-08-02T21:43:25.906437Z

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Observation be2fb79c-5ff0-4979-8cdc-d9b4304253ac · outbound

This paper cites Nash,C 1 isometric imbeddings, Ann.

Sharp non-uniqueness for the Navier-Stokes equations in scaling critical spaces Nash,C 1 isometric imbeddings, Ann

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Resolution: unresolved; no resolver link, observed 2026-08-02T21:43:26.017847Z

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Observation 55fb8610-7d2e-4f7f-a804-9132691b782b · outbound

This paper cites Palasek,Non-uniqueness in the Leray-Hopf class for a dyadic Navier-Stokes model, Int.

Sharp non-uniqueness for the Navier-Stokes equations in scaling critical spaces Palasek,Non-uniqueness in the Leray-Hopf class for a dyadic Navier-Stokes model, Int

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Resolution: unresolved; no resolver link, observed 2026-08-02T21:43:26.140761Z

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Observation ea06f4de-e7aa-48c0-bb23-998c3d5e4630 · outbound

This paper cites Planchon,Asymptotic behavior of global solutions to the Navier-Stokes equations inR3, Rev.

Sharp non-uniqueness for the Navier-Stokes equations in scaling critical spaces Planchon,Asymptotic behavior of global solutions to the Navier-Stokes equations inR3, Rev

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Resolution: unresolved; no resolver link, observed 2026-08-02T21:43:26.273057Z

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Observation f4b2246f-942d-4e40-9b10-ea339e9cf194 · outbound

This paper cites Sawano,Theory of Besov spaces, Developments in Mathematics, vol.

Sharp non-uniqueness for the Navier-Stokes equations in scaling critical spaces Sawano,Theory of Besov spaces, Developments in Mathematics, vol

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Observation 329e749f-0086-4b54-aa5b-cbe3017cf6e3 · outbound

This paper cites Serrin,The initial value problem for the Navier-Stokes equations, Nonlinear Problems (Proc.

Sharp non-uniqueness for the Navier-Stokes equations in scaling critical spaces Serrin,The initial value problem for the Navier-Stokes equations, Nonlinear Problems (Proc

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Resolution: unresolved; no resolver link, observed 2026-08-02T21:43:26.523160Z

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Observation 60dd6fed-b51d-49e3-871e-a590b6566cc7 · outbound

This paper cites Takeuchi,Decay rates of small global solutions to the Navier–Stokes system in scaling invariant homogeneous Besov spaces, Math.

Sharp non-uniqueness for the Navier-Stokes equations in scaling critical spaces Takeuchi,Decay rates of small global solutions to the Navier–Stokes system in scaling invariant homogeneous Besov spaces, Math

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Resolution: unresolved; no resolver link, observed 2026-08-02T21:43:26.637766Z

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Observation 5d751441-7bc2-4197-9c08-3141d4fb135d · outbound

This paper cites an unresolved cited work.

Sharp non-uniqueness for the Navier-Stokes equations in scaling critical spaces Unresolved cited work

Reference 56

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Observation 5a970426-439f-44da-a6dc-603cc8e90b04 · outbound

This paper cites an unresolved cited work.

Sharp non-uniqueness for the Navier-Stokes equations in scaling critical spaces Unresolved cited work

Reference 57

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Observation 71eeabe8-c901-4fed-99fc-aab8e8ea303a · outbound

This paper cites Tsurumi,Well-posedness and ill-posedness problems of the stationary Navier-Stokes equa- tions in scaling invariant Besov spaces, Arch.

Sharp non-uniqueness for the Navier-Stokes equations in scaling critical spaces Tsurumi,Well-posedness and ill-posedness problems of the stationary Navier-Stokes equa- tions in scaling invariant Besov spaces, Arch

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Resolution: unresolved; no resolver link, observed 2026-08-02T21:43:26.827447Z

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Observation 109506cb-f725-40cc-a5e5-46deb22f1d95 · outbound

This paper cites Wang,Ill-posedness for the Navier-Stokes equations in critical Besov spaces˙B−1 ∞,q, Adv.

Sharp non-uniqueness for the Navier-Stokes equations in scaling critical spaces Wang,Ill-posedness for the Navier-Stokes equations in critical Besov spaces˙B−1 ∞,q, Adv

Reference 59

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Observation c4a9c0e2-c4ed-4b91-aabc-ce41de8e7f61 · outbound

This paper cites Watanabe,Algebraic decay rates for strong solutions to the Navier–Stokes equations in critical spaces(2025).

Sharp non-uniqueness for the Navier-Stokes equations in scaling critical spaces Watanabe,Algebraic decay rates for strong solutions to the Navier–Stokes equations in critical spaces(2025)

Reference 60

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Observation a0148e0a-eab5-4cc2-b9cd-bd6316d20210 · outbound

This paper cites Ann.317(2000), 635–675.

Sharp non-uniqueness for the Navier-Stokes equations in scaling critical spaces Ann.317(2000), 635–675

Reference 61

Resolution: unresolved; no resolver link, observed 2026-08-02T21:43:27.065292Z

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Observation c0c73c15-d0fd-4b49-badd-0b92c4de9b14 · outbound

This paper cites Yoneda,Ill-posedness of the 3D-Navier-Stokes equations in a generalized Besov space near BMO−1, J.

Sharp non-uniqueness for the Navier-Stokes equations in scaling critical spaces Yoneda,Ill-posedness of the 3D-Navier-Stokes equations in a generalized Besov space near BMO−1, J

Reference 62

Resolution: unresolved; no resolver link, observed 2026-08-02T21:43:27.124521Z

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Observation 527c0898-d9cf-4b01-9fc8-b8cf936436b4 · outbound

This paper cites Uniqueness of mild solutions to the Navier-Stokes equations in weak-type $L^d$ space.

Sharp non-uniqueness for the Navier-Stokes equations in scaling critical spaces Uniqueness of mild solutions to the Navier-Stokes equations in weak-type $L^d$ space

Reference 63

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Pith citing papers

Observation ac7b9802-cc64-4cc6-adf6-51416c7f947d · inbound

On non-uniqueness of mild solutions and stationary singular solutions to the Navier-Stokes equations cites this paper.

On non-uniqueness of mild solutions and stationary singular solutions to the Navier-Stokes equations Sharp non-uniqueness for the Navier-Stokes equations in scaling critical spaces

Reference 2026

Resolution: unresolved; no resolver link, observed 2026-08-02T19:14:29.482666Z

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Observation 5da917be-fff7-4997-8ff8-81f892e4f1ac · inbound

Uniqueness of the dissipative SQG without time-continuity assumption cites this paper.

Uniqueness of the dissipative SQG without time-continuity assumption Sharp non-uniqueness for the Navier-Stokes equations in scaling critical spaces

Reference 19

Resolution: verified exact; local_arxiv, observed 2026-07-03T15:58:38.281959Z

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