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Paper Citation Record · LEDGER

$(H,H^2)$-smoothing effect of Navier-Stokes equations with additive white noise on two-dimensional torus

As of 22 August 2026, this Paper Citation Record lists 44 of 44 outbound references and 0 inbound Pith citation observations for arXiv:2508.18745.

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

pith.paper-citation-record.v1
2508.18745 v1

Coverage vector

measured 44 of 44 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-15T17:03:36.442197Z

measured 44 of 44 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-22T06:32:14.747728+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

44 of 44 outbound references displayed

  • verified exact0
  • verified fuzzy40
  • unresolved4
  • parse uncertain0
  • malformed identifier0
  • metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation d219d3d0-f03c-4efa-994b-9b13f2758a64 · outbound

This paper cites Arnold, Random Dynamical Systems, Springer-Verlag, Berlin, 1998.

$(H,H^2)$-smoothing effect of Navier-Stokes equations with additive white noise on two-dimensional torus Arnold, Random Dynamical Systems, Springer-Verlag, Berlin, 1998

Reference 1

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T17:03:37.201626Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

source=pdf_text observed=2026-08-15T17:03:35.533065Z digest=sha256:781e247039fd44788c3e7f343cab1efb8fda120f94b9b52075b3a07eddf5d6f6

Observation 5a0dcf94-5599-4fbe-a234-5d91f34a573f · outbound

This paper cites Brze ´zniak, T.

$(H,H^2)$-smoothing effect of Navier-Stokes equations with additive white noise on two-dimensional torus Brze ´zniak, T

Reference 2

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T17:03:37.184919Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

source=pdf_text observed=2026-08-15T17:03:35.539186Z digest=sha256:106e5783ab10046664f4ca0bb120b16ed7818f5fb2b673aef0fe45fba5c086e2

Observation 0835f4fc-02e2-4cbb-a114-6066190dfaa9 · outbound

This paper cites Brze ´zniak, B.

$(H,H^2)$-smoothing effect of Navier-Stokes equations with additive white noise on two-dimensional torus Brze ´zniak, B

Reference 3

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T17:03:37.171036Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

source=pdf_text observed=2026-08-15T17:03:35.543352Z digest=sha256:84abe4bd5048c69dc2e5d52610c64d789ea40861b636bc5c3dc0b0ffef9566b6

Observation 89f242f9-5921-4f3a-bf5a-31fd0f0fdb1a · outbound

This paper cites Brze ´zniak, B.

$(H,H^2)$-smoothing effect of Navier-Stokes equations with additive white noise on two-dimensional torus Brze ´zniak, B

Reference 4

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T17:03:37.157979Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

source=pdf_text observed=2026-08-15T17:03:35.547700Z digest=sha256:b8f9c2dc81057e878b71f6125a840624484be3337e874153c7b592cf17b4d90f

Observation 916814ba-32d6-47e6-a404-d7e50aaa69d3 · outbound

This paper cites Brze ´zniak, Y .H.

$(H,H^2)$-smoothing effect of Navier-Stokes equations with additive white noise on two-dimensional torus Brze ´zniak, Y .H

Reference 5

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T17:03:37.140709Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

source=pdf_text observed=2026-08-15T17:03:35.552637Z digest=sha256:fad35bb040f6d22619e21a0f67a44c3842a7d5f2d718c6ace89338fa7cb732d4

Observation 16e1f3bf-7683-4954-9156-9541f0525871 · outbound

This paper cites an unresolved cited work.

$(H,H^2)$-smoothing effect of Navier-Stokes equations with additive white noise on two-dimensional torus Unresolved cited work

Reference 6

Resolution
unresolved
raw_fallback, observed 2026-08-15T17:03:37.127634Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

source=pdf_text observed=2026-08-15T17:03:35.594215Z digest=sha256:81e90b5eaba63b8ec23720d45521d801164a2356143214ee5dfc164abe1216e7

Observation 990be251-ce87-4334-9b01-4da7d186d61d · outbound

This paper cites Bollettino della Unione Matematica Italiana.

$(H,H^2)$-smoothing effect of Navier-Stokes equations with additive white noise on two-dimensional torus Bollettino della Unione Matematica Italiana

Reference 7

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T17:03:37.114397Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

source=pdf_text observed=2026-08-15T17:03:35.652191Z digest=sha256:3ec4d521e747f3463905e3c43a8066eea4fba75e740e4890e3e5b305e317cd4b

Observation edc845be-3c3d-4528-863f-7a60fb64147f · outbound

This paper cites Constantin, C.

$(H,H^2)$-smoothing effect of Navier-Stokes equations with additive white noise on two-dimensional torus Constantin, C

Reference 8

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T17:03:37.100080Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

source=pdf_text observed=2026-08-15T17:03:35.724548Z digest=sha256:54abdfea51f82806df93fdcf3dc4d635a1ccf6ade158679e7fcaf7a9d5ea2a0c

Observation 52e8c4d0-735f-4ce0-a24a-ddff17d84fb0 · outbound

This paper cites Crauel, A.

$(H,H^2)$-smoothing effect of Navier-Stokes equations with additive white noise on two-dimensional torus Crauel, A

Reference 9

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T17:03:37.085559Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

source=pdf_text observed=2026-08-15T17:03:35.795973Z digest=sha256:6ced39368d8ad65a4c8c5c33b6a156cf3acf0baa7b8952c278522ac4d0fc9e22

Observation a4ee0d83-6f83-496a-9173-91d893e36e19 · outbound

This paper cites Crauel, F.

$(H,H^2)$-smoothing effect of Navier-Stokes equations with additive white noise on two-dimensional torus Crauel, F

Reference 10

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T17:03:37.070047Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

source=pdf_text observed=2026-08-15T17:03:35.873357Z digest=sha256:07f4fb8dab8c1eb5159868fe58eb823d5dc5fe2630f99d72531c8458dae56feb

Observation e5136612-4688-4ecf-b9bf-f0c92d4baefc · outbound

This paper cites Cui, A.N.

$(H,H^2)$-smoothing effect of Navier-Stokes equations with additive white noise on two-dimensional torus Cui, A.N

Reference 11

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T17:03:37.052344Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

source=pdf_text observed=2026-08-15T17:03:35.908878Z digest=sha256:214db11ac6c8b185860fa02783ad6d51a81a6ffba203e7dc3abf73a0ce2b0c7b

Observation 69b2673d-4a44-4177-927d-0207056526fc · outbound

This paper cites Cui, R.N.

$(H,H^2)$-smoothing effect of Navier-Stokes equations with additive white noise on two-dimensional torus Cui, R.N

Reference 12

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T17:03:37.035036Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

source=pdf_text observed=2026-08-15T17:03:35.962119Z digest=sha256:543e5ee53fbcdba2774925b12bff722ab5e953990974b0937edb562f6abf476a

Observation e309ac21-b637-47d6-8363-dcb5bdc43a5b · outbound

This paper cites Cui, R.N.

$(H,H^2)$-smoothing effect of Navier-Stokes equations with additive white noise on two-dimensional torus Cui, R.N

Reference 13

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T17:03:37.021162Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

source=pdf_text observed=2026-08-15T17:03:36.026611Z digest=sha256:91437498c63f2360f55c09e058a47445e9a3daf6bb7ece2cf1985a9ae886b2fc

Observation 3f40dac2-448c-4984-b08e-95152f882ddd · outbound

This paper cites Cui, J.A.

$(H,H^2)$-smoothing effect of Navier-Stokes equations with additive white noise on two-dimensional torus Cui, J.A

Reference 14

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T17:03:37.003023Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

source=pdf_text observed=2026-08-15T17:03:36.031398Z digest=sha256:ff71d731b02beed7707f03621a75a3895b5fd88a156a56d12da9bd904a54bfe6

Observation 85313801-40cb-414f-b8ed-cfbb9e0a154b · outbound

This paper cites Cui, Y .R.

$(H,H^2)$-smoothing effect of Navier-Stokes equations with additive white noise on two-dimensional torus Cui, Y .R

Reference 15

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T17:03:36.987752Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

source=pdf_text observed=2026-08-15T17:03:36.035983Z digest=sha256:e2abe9c7ebdbec258d19f78abb26d20136bc9202ee78bf9890cf3c7ee56ba82d

Observation 246d70e2-675f-4624-b2a8-2102bf7004c9 · outbound

This paper cites Dong, Random attractors for stochastic Navier-Stokes equation on a 2D rotating sphere with stable L´evy noise, Discrete Contin.

$(H,H^2)$-smoothing effect of Navier-Stokes equations with additive white noise on two-dimensional torus Dong, Random attractors for stochastic Navier-Stokes equation on a 2D rotating sphere with stable L´evy noise, Discrete Contin

Reference 16

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T17:03:36.974656Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

source=pdf_text observed=2026-08-15T17:03:36.039674Z digest=sha256:7ecef87bac60f00bc4e275b8e7021caace7cb0cf99f22d7b86359280bbc617aa

Observation 99b124f4-520f-4d80-9ff4-23f97434a4a8 · outbound

This paper cites Garc ´ıa-Luengo, P.

$(H,H^2)$-smoothing effect of Navier-Stokes equations with additive white noise on two-dimensional torus Garc ´ıa-Luengo, P

Reference 17

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T17:03:36.962453Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

source=pdf_text observed=2026-08-15T17:03:36.043131Z digest=sha256:a821bba25f9c574d5ba053dbaad2959e9bd3785a932e163f47b791a98fcf2eaf

Observation e62312ff-a05d-4178-a516-634a188f0b41 · outbound

This paper cites Hou, K.T.

$(H,H^2)$-smoothing effect of Navier-Stokes equations with additive white noise on two-dimensional torus Hou, K.T

Reference 18

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T17:03:36.952198Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

source=pdf_text observed=2026-08-15T17:03:36.047274Z digest=sha256:979e863c96e23793510a2221ce92cca8c73e01b6212db37d813a12ab999d021d

Observation f7af7271-804d-4852-916f-10fb9c8f5456 · outbound

This paper cites Ju, The H1-compact global attractor for the solutions to the Navier-Stokes equations in two- dimensional unbounded domains, Nonlinearity, 13 (2000), 1227-1238.

$(H,H^2)$-smoothing effect of Navier-Stokes equations with additive white noise on two-dimensional torus Ju, The H1-compact global attractor for the solutions to the Navier-Stokes equations in two- dimensional unbounded domains, Nonlinearity, 13 (2000), 1227-1238

Reference 19

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T17:03:36.939093Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

source=pdf_text observed=2026-08-15T17:03:36.050897Z digest=sha256:2251efa30aed9cb4c317ba27657b947061c4eda9d9cad27907bf8b54bd9108e8

Observation 38131520-454b-4619-82c7-99a28840defa · outbound

This paper cites Lady ˘zenskaja, Solution ”in the large” of the nonstationary boundary value problem for the Navier-Stokes system with two space variables, Comm.

$(H,H^2)$-smoothing effect of Navier-Stokes equations with additive white noise on two-dimensional torus Lady ˘zenskaja, Solution ”in the large” of the nonstationary boundary value problem for the Navier-Stokes system with two space variables, Comm

Reference 20

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T17:03:36.923002Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

source=pdf_text observed=2026-08-15T17:03:36.055399Z digest=sha256:63280c9c1126265438ba53ac27d10ff381ce021799c711937998215a7b48cfcc

Observation 404905ea-6f1a-424a-81d6-c0b95a12eb6d · outbound

This paper cites Langa, G.

$(H,H^2)$-smoothing effect of Navier-Stokes equations with additive white noise on two-dimensional torus Langa, G

Reference 21

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T17:03:36.909180Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

source=pdf_text observed=2026-08-15T17:03:36.059964Z digest=sha256:f8a2227b3a36063e3954fcf05c8565c66c468aa380191d84d3dc2d821fbd82e8

Observation 1a4f9212-d476-4279-8801-6207b4b954bf · outbound

This paper cites Langa, J.C.

$(H,H^2)$-smoothing effect of Navier-Stokes equations with additive white noise on two-dimensional torus Langa, J.C

Reference 22

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T17:03:36.888323Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

source=pdf_text observed=2026-08-15T17:03:36.064537Z digest=sha256:13945a3e9ca6235ead0c15d32554466b7e55419a00adee195009961ff16ea677

Observation cd7fb28e-042c-48fd-ad78-cd839ce47390 · outbound

This paper cites Li, Uniform random attractors for 2D non-autonomous stochastic Navier-Stokes equations , J.

$(H,H^2)$-smoothing effect of Navier-Stokes equations with additive white noise on two-dimensional torus Li, Uniform random attractors for 2D non-autonomous stochastic Navier-Stokes equations , J

Reference 23

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T17:03:36.874096Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

source=pdf_text observed=2026-08-15T17:03:36.070317Z digest=sha256:8df74020744d4f1fb63edf202125cd631b3fcee014df9195bf9e33cda7dab436

Observation 67f51e56-35d4-4abe-a7fa-347c10558b8c · outbound

This paper cites Liu, H.J.

$(H,H^2)$-smoothing effect of Navier-Stokes equations with additive white noise on two-dimensional torus Liu, H.J

Reference 24

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T17:03:36.853215Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

source=pdf_text observed=2026-08-15T17:03:36.075640Z digest=sha256:06cf25d6867c28dc0b2a153d7f57eeb11586c148428ea32abb23be8d0d5183dc

Observation 006c108d-1233-4149-9f75-89b7d82abdf0 · outbound

This paper cites Liu, Instability for the Navier-Stokes equations on the 2-dimensional torus and a lower bound for the Hausdorff dimension of their global attractors, Comm.

$(H,H^2)$-smoothing effect of Navier-Stokes equations with additive white noise on two-dimensional torus Liu, Instability for the Navier-Stokes equations on the 2-dimensional torus and a lower bound for the Hausdorff dimension of their global attractors, Comm

Reference 25

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T17:03:36.837432Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

source=pdf_text observed=2026-08-15T17:03:36.080002Z digest=sha256:9c77b23ff16e3740da44cb7fa9d34e39cfe5c38232298aa7bc99e015638f86b3

Observation 982e8d0e-845e-4b4b-a9d7-d82a14eea76f · outbound

This paper cites Liu,A sharp lower bound for the Hausdorff dimension of the global attractors of the 2D Navier- Stokes equations, Comm.

$(H,H^2)$-smoothing effect of Navier-Stokes equations with additive white noise on two-dimensional torus Liu,A sharp lower bound for the Hausdorff dimension of the global attractors of the 2D Navier- Stokes equations, Comm

Reference 26

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T17:03:36.822056Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

source=pdf_text observed=2026-08-15T17:03:36.084502Z digest=sha256:e260601a6f6cd6c3cf0491e8321f430a4082e0741c018afc30f5a027b95589c8

Observation cc4627e7-4919-4f17-8a1d-3cfa4631a504 · outbound

This paper cites an unresolved cited work.

$(H,H^2)$-smoothing effect of Navier-Stokes equations with additive white noise on two-dimensional torus Unresolved cited work

Reference 27

Resolution
unresolved
raw_fallback, observed 2026-08-15T17:03:36.808777Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

source=pdf_text observed=2026-08-15T17:03:36.088354Z digest=sha256:2a53cc34a62b31831c3789ed24afb9ed374bc3d13b5fd8b4ed92a01cde2c5012

Observation 89dac4c2-5b8d-405c-9a43-aa70e8e47899 · outbound

This paper cites Łukaszewicz, Pullback attractors and statistical solutions for 2-D Navier-Stokes equations , Dis- crete Contin.

$(H,H^2)$-smoothing effect of Navier-Stokes equations with additive white noise on two-dimensional torus Łukaszewicz, Pullback attractors and statistical solutions for 2-D Navier-Stokes equations , Dis- crete Contin

Reference 28

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T17:03:36.795057Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

source=pdf_text observed=2026-08-15T17:03:36.092156Z digest=sha256:b57df2ff74c1ac1413a8ab58eeda1984db0e3ac00fba3feb918817e7ef3a238b

Observation f8a2b62e-c955-48fe-85fd-eedbd1a1f1a3 · outbound

This paper cites Mohammed, T.S.

$(H,H^2)$-smoothing effect of Navier-Stokes equations with additive white noise on two-dimensional torus Mohammed, T.S

Reference 29

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T17:03:36.781362Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

source=pdf_text observed=2026-08-15T17:03:36.095927Z digest=sha256:fd46cba4d866d918593422d19ec57f7b8a0252672c8b1a4b74bd4135acf86287

Observation 6fa11d82-4916-49cd-8259-ea92250ab41a · outbound

This paper cites Rosa, The global attractor for the 2D Navier-Stokes flow on some unbounded domains , Nonlinear Anal., 32 (1998), 71-85.

$(H,H^2)$-smoothing effect of Navier-Stokes equations with additive white noise on two-dimensional torus Rosa, The global attractor for the 2D Navier-Stokes flow on some unbounded domains , Nonlinear Anal., 32 (1998), 71-85

Reference 30

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T17:03:36.768778Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

source=pdf_text observed=2026-08-15T17:03:36.100635Z digest=sha256:dd79ea60bbd374b91c76ced792671f325ab59da252c30ea8ad300a5921a21ae1

Observation 363168e2-7e78-49e6-b0f7-b016338da35e · outbound

This paper cites Robinson, Infinite-Dimensional Dynamical Systems: An Introduction to Dissipative Parabolic PDEs and the Theory of Global Attractors, vol.

$(H,H^2)$-smoothing effect of Navier-Stokes equations with additive white noise on two-dimensional torus Robinson, Infinite-Dimensional Dynamical Systems: An Introduction to Dissipative Parabolic PDEs and the Theory of Global Attractors, vol

Reference 31

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T17:03:36.754617Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

source=pdf_text observed=2026-08-15T17:03:36.105010Z digest=sha256:2d6d836a8fa33735b26b1d17d263768c9cc5b9a3397ec02ce99fa93e248b3202

Observation 33ad9149-de4d-4e6f-bb5d-c9f46a3c842c · outbound

This paper cites Robinson, Dimensions, Embeddings, and Attractors, Cambridge University Press, 2011.

$(H,H^2)$-smoothing effect of Navier-Stokes equations with additive white noise on two-dimensional torus Robinson, Dimensions, Embeddings, and Attractors, Cambridge University Press, 2011

Reference 32

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T17:03:36.741014Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

source=pdf_text observed=2026-08-15T17:03:36.108535Z digest=sha256:47e93867a3283a32e14c2bcf4574d80156507f0c8cc38ef3d31aad80738991c8

Observation 62fd8fc3-1187-4e17-a9a9-fe0a23ea7174 · outbound

This paper cites Robinson, Attractors and Finite-Dimensional Behaviour in the 2D Navier-Stokes Equations , ISRN Mathematical Analysis 2013, Article ID 291823, 29 pages.

$(H,H^2)$-smoothing effect of Navier-Stokes equations with additive white noise on two-dimensional torus Robinson, Attractors and Finite-Dimensional Behaviour in the 2D Navier-Stokes Equations , ISRN Mathematical Analysis 2013, Article ID 291823, 29 pages

Reference 33

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T17:03:36.726977Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

source=pdf_text observed=2026-08-15T17:03:36.112670Z digest=sha256:4a4f89660dc706ce376a1c595afc24cafcd8c49b4584b1c5ff00cd648dd5b29b

Observation dd7ae12e-5e19-40b3-bc5e-54338de90368 · outbound

This paper cites Song, Y .R.

$(H,H^2)$-smoothing effect of Navier-Stokes equations with additive white noise on two-dimensional torus Song, Y .R

Reference 34

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T17:03:36.714160Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

source=pdf_text observed=2026-08-15T17:03:36.116939Z digest=sha256:06e42f223c62620604e8e68079cc52d80c1ef60ed321813ebabb9ac65a222a99

Observation 456cf55d-8e48-43a5-b8c2-8b1f1d9853e0 · outbound

This paper cites Sun, Asymptotic regularity for some dissipative equations , J.

$(H,H^2)$-smoothing effect of Navier-Stokes equations with additive white noise on two-dimensional torus Sun, Asymptotic regularity for some dissipative equations , J

Reference 35

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T17:03:36.701595Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

source=pdf_text observed=2026-08-15T17:03:36.120921Z digest=sha256:672b25902e9ac404816cd4ab759d825027b8066ac4b4b67819fa4c373404a1f8

Observation 434879b3-760d-4575-99b3-d834573cb749 · outbound

This paper cites Temam, Infinite-dimensional dynamical systems in mechanics and physics.

$(H,H^2)$-smoothing effect of Navier-Stokes equations with additive white noise on two-dimensional torus Temam, Infinite-dimensional dynamical systems in mechanics and physics

Reference 36

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T17:03:36.604425Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

source=pdf_text observed=2026-08-15T17:03:36.125335Z digest=sha256:c3b0e39fc54138bb5d530fc5640612ac1a948b7e1c29fb8c54993b0355076015

Observation 6c5fa092-9cd4-4668-8f38-6bd3f89f284d · outbound

This paper cites Temam, Navier-Stokes Equations: Theory and Numerical Analysis, vol.

$(H,H^2)$-smoothing effect of Navier-Stokes equations with additive white noise on two-dimensional torus Temam, Navier-Stokes Equations: Theory and Numerical Analysis, vol

Reference 37

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T17:03:36.579223Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

source=pdf_text observed=2026-08-15T17:03:36.134280Z digest=sha256:e20acfcae649e381a2e3f24fb8c6dc20234e46967bf9a1d35a07b1391a10544b

Observation dce31003-defb-42f9-b34d-a53e5195dda5 · outbound

This paper cites Wang, Periodic random attractors for stochastic Navier-Stokes equations on unbounded do- mains, Electron.

$(H,H^2)$-smoothing effect of Navier-Stokes equations with additive white noise on two-dimensional torus Wang, Periodic random attractors for stochastic Navier-Stokes equations on unbounded do- mains, Electron

Reference 38

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T17:03:36.554834Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

source=pdf_text observed=2026-08-15T17:03:36.183486Z digest=sha256:1bbbf9b301e79b7c083f26c0898f2b025834d477dd104aff21cc0e87a52f38a3

Observation 1adacd68-46db-4ce7-8be8-5304486e9822 · outbound

This paper cites Wang, Uniform tail-ends estimates of the Navier-Stokes equations on unbounded channel-like domains, Proc.

$(H,H^2)$-smoothing effect of Navier-Stokes equations with additive white noise on two-dimensional torus Wang, Uniform tail-ends estimates of the Navier-Stokes equations on unbounded channel-like domains, Proc

Reference 39

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T17:03:36.540891Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

source=pdf_text observed=2026-08-15T17:03:36.297223Z digest=sha256:f0a5c4141c8bd171223e33c6a16fee3541da95b51774a9f0a0feb5cbe40351e0

Observation 07945a15-4224-4282-b8a8-7a6a17aac717 · outbound

This paper cites Wang, B.L.

$(H,H^2)$-smoothing effect of Navier-Stokes equations with additive white noise on two-dimensional torus Wang, B.L

Reference 40

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T17:03:36.527379Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

source=pdf_text observed=2026-08-15T17:03:36.378155Z digest=sha256:ec38f5117dd422d68f601bb31812093b2408f74318dd74b3350db0ef6e279e86

Observation e35dfd69-3561-4163-b13f-0bf31a599b94 · outbound

This paper cites an unresolved cited work.

$(H,H^2)$-smoothing effect of Navier-Stokes equations with additive white noise on two-dimensional torus Unresolved cited work

Reference 41

Resolution
unresolved
raw_fallback, observed 2026-08-15T17:03:36.515346Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

source=pdf_text observed=2026-08-15T17:03:36.427462Z digest=sha256:796531fb0ce6eb2b2a42c8e82043e71c926e54900a573777583267c9450491b2

Observation fbea8d1b-29e4-4e55-b55c-24686f41eef2 · outbound

This paper cites Yang, Y .M.

$(H,H^2)$-smoothing effect of Navier-Stokes equations with additive white noise on two-dimensional torus Yang, Y .M

Reference 42

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T17:03:36.501927Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

source=pdf_text observed=2026-08-15T17:03:36.432981Z digest=sha256:0139c99fd0b0c031f4074ab961895bb4c2a4a2bec842674c561762f5e1fff819

Observation 6fca62ba-c71c-4da4-af14-e5d583279958 · outbound

This paper cites an unresolved cited work.

$(H,H^2)$-smoothing effect of Navier-Stokes equations with additive white noise on two-dimensional torus Unresolved cited work

Reference 43

Resolution
unresolved
raw_fallback, observed 2026-08-15T17:03:36.490019Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

source=pdf_text observed=2026-08-15T17:03:36.438173Z digest=sha256:514240ee6204249e0bd2c378b6f7eb2074334149576f9365d4c0b6a550e323b0

Observation 38427453-c0a8-49bd-ad62-999c97c64682 · outbound

This paper cites Zhao, J.Q.

$(H,H^2)$-smoothing effect of Navier-Stokes equations with additive white noise on two-dimensional torus Zhao, J.Q

Reference 44

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T17:03:36.476992Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

source=pdf_text observed=2026-08-15T17:03:36.442197Z digest=sha256:386da5c13f5c1776861ee56e8f7ba86d154e9e11ef29627bb1534d7227adb1b5

Pith citing papers

No inbound Pith citation observations are available.