Paper Citation Record · LEDGER

Non-uniqueness of (Stochastic) Lagrangian Trajectories for Euler Equations

As of 17 August 2026, this Paper Citation Record lists 49 of 49 outbound references and 1 inbound Pith citation observation for arXiv:2504.16687.

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

pith.paper-citation-record.v1
2504.16687 v2

Coverage vector

measured 49 of 49 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-16T11:10:36.665719Z

measured 50 of 50 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-17T06:30:58.91139+00:00

measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-07-01T04:15:55.096633Z

measured 0 of 1 external citation measurements

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

Source: arxiv_reference, observed 2026-07-01T11:35:43.512457Z

Reference resolution

49 of 49 outbound references displayed

verified exact5
verified fuzzy16
unresolved26
parse uncertain0
malformed identifier2
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External citation measurements

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Outbound references

Observation 83f0e596-3461-4992-84bb-c793c75a9cd2 · outbound

This paper cites [BDLIS15] T.

Non-uniqueness of (Stochastic) Lagrangian Trajectories for Euler Equations [BDLIS15] T

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T11:10:37.606419Z

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No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 58eeb5b1-8cb9-423a-a16e-d425540bfc07 · outbound

This paper cites Butkovsky, S.

Non-uniqueness of (Stochastic) Lagrangian Trajectories for Euler Equations Butkovsky, S

Reference 8

Resolution: unresolved; no resolver link, observed 2026-08-16T11:10:36.444721Z

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Observation 7d1d6ada-f9df-4309-ba7a-c73c1b2fbd05 · outbound

This paper cites Anomalous dissipation and Euler flows.

Non-uniqueness of (Stochastic) Lagrangian Trajectories for Euler Equations Anomalous dissipation and Euler flows

Reference 10

Resolution: malformed identifier; no resolver link, observed 2026-08-16T11:10:36.455712Z

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Observation 1508a3f0-b80e-4042-aad6-225b4c25d597 · outbound

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

Non-uniqueness of (Stochastic) Lagrangian Trajectories for Euler Equations Global dissipative solutions of the 3D Naiver-Stokes and MHD equations

Reference 13

Resolution: unresolved; no resolver link, observed 2026-08-16T11:10:36.483181Z

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Observation 96c1e0eb-9033-4a6f-8b7f-556bbafaae4f · outbound

This paper cites Cheskidov, and X.

Non-uniqueness of (Stochastic) Lagrangian Trajectories for Euler Equations Cheskidov, and X

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T11:10:37.557315Z

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Observation c5057f5e-c897-4bc1-8733-520cb5cb0c15 · outbound

This paper cites A note on weak existence for singular SDEs.

Non-uniqueness of (Stochastic) Lagrangian Trajectories for Euler Equations A note on weak existence for singular SDEs

Reference 19

Resolution: verified exact; local_arxiv, observed 2026-08-16T11:10:37.051792Z

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No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation f57989ba-2cbd-45f2-acbf-f69d82f9d295 · outbound

This paper cites Almost-everywhere uniqueness of Lagrangian trajectories for $3$D Navier--Stokes revisited.

Non-uniqueness of (Stochastic) Lagrangian Trajectories for Euler Equations Almost-everywhere uniqueness of Lagrangian trajectories for $3$D Navier--Stokes revisited

Reference 20

Resolution: verified exact; local_arxiv, observed 2026-08-16T11:10:37.027291Z

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No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation ef08a86f-11a8-4a58-982a-a2caefc0f365 · outbound

This paper cites Galeati, M.

Non-uniqueness of (Stochastic) Lagrangian Trajectories for Euler Equations Galeati, M

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T11:10:37.492691Z

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Observation 1de8c932-f74e-4289-87e9-90f69ae48e58 · outbound

This paper cites an unresolved cited work.

Non-uniqueness of (Stochastic) Lagrangian Trajectories for Euler Equations Unresolved cited work

Reference 22

Resolution: unresolved; raw_fallback, observed 2026-08-16T11:10:37.477278Z

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Observation 419caf00-8773-4414-8470-cbf1c69daa80 · outbound

This paper cites Weak well-posedness of energy solutions to singular SDEs with supercritical distributional drift.

Non-uniqueness of (Stochastic) Lagrangian Trajectories for Euler Equations Weak well-posedness of energy solutions to singular SDEs with supercritical distributional drift

Reference 23

Resolution: unresolved; no resolver link, observed 2026-08-16T11:10:36.526430Z

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Observation dfaffe11-d348-465f-ac35-fa8863208897 · outbound

This paper cites an unresolved cited work.

Non-uniqueness of (Stochastic) Lagrangian Trajectories for Euler Equations Unresolved cited work

Reference 24

Resolution: unresolved; raw_fallback, observed 2026-08-16T11:10:37.461083Z

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Observation 4d643137-7b79-46ef-82f6-98cd3ab62316 · outbound

This paper cites Anomalous and total dissipation due to advection by solutions of randomly forced Navier-Stokes equations.

Non-uniqueness of (Stochastic) Lagrangian Trajectories for Euler Equations Anomalous and total dissipation due to advection by solutions of randomly forced Navier-Stokes equations

Reference 25

Resolution: unresolved; no resolver link, observed 2026-08-16T11:10:36.536711Z

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Observation ae8feeeb-e07c-42e0-99b4-652d34c1302f · outbound

This paper cites Distribution-flow dependent SDEs driven by (fractional) Brownian motion and Navier-Stokes equations.

Non-uniqueness of (Stochastic) Lagrangian Trajectories for Euler Equations Distribution-flow dependent SDEs driven by (fractional) Brownian motion and Navier-Stokes equations

Reference 26

Resolution: unresolved; no resolver link, observed 2026-08-16T11:10:36.541815Z

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Observation 5ffc4de0-1215-40ff-908d-7287cc846cb1 · outbound

This paper cites Hofmanov´ a, R.

Non-uniqueness of (Stochastic) Lagrangian Trajectories for Euler Equations Hofmanov´ a, R

Reference 28

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T11:10:37.443139Z

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Observation 7ddf2154-ae6f-4252-88ae-b338535d75a8 · outbound

This paper cites an unresolved cited work.

Non-uniqueness of (Stochastic) Lagrangian Trajectories for Euler Equations Unresolved cited work

Reference 31

Resolution: unresolved; raw_fallback, observed 2026-08-16T11:10:37.409239Z

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Observation 7319a466-e28f-4a9b-9d6b-7b1f8e792d32 · outbound

This paper cites On stochastic It\^o processes with drift in $L_{d}$.

Non-uniqueness of (Stochastic) Lagrangian Trajectories for Euler Equations On stochastic It\^o processes with drift in $L_{d}$

Reference 33

Resolution: unresolved; no resolver link, observed 2026-08-16T11:10:36.578614Z

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Observation 0f67c7d3-dc0b-4547-b16f-fed09c730bd7 · outbound

This paper cites On strong solutions of It\^o's equations with a$\,\in W^{1}_{d}$ and b$\,\in L_{d}$.

Non-uniqueness of (Stochastic) Lagrangian Trajectories for Euler Equations On strong solutions of It\^o's equations with a$\,\in W^{1}_{d}$ and b$\,\in L_{d}$

Reference 34

Resolution: unresolved; no resolver link, observed 2026-08-16T11:10:36.584422Z

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Observation 0b6d9713-5566-49d1-9f39-49fa111d24e2 · outbound

This paper cites an unresolved cited work.

Non-uniqueness of (Stochastic) Lagrangian Trajectories for Euler Equations Unresolved cited work

Reference 35

Resolution: unresolved; raw_fallback, observed 2026-08-16T11:10:37.393362Z

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No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 61a2917b-b255-42cb-ab09-c4053351ca83 · outbound

This paper cites L ¨ u, X.

Non-uniqueness of (Stochastic) Lagrangian Trajectories for Euler Equations L ¨ u, X

Reference 37

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T11:10:37.375800Z

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No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 582873c9-d521-4e24-b550-d52b332c7149 · outbound

This paper cites Non-uniqueness of weak solutions to the Navier-Stokes equations in R^3.

Non-uniqueness of (Stochastic) Lagrangian Trajectories for Euler Equations Non-uniqueness of weak solutions to the Navier-Stokes equations in R^3

Reference 40

Resolution: unresolved; no resolver link, observed 2026-08-16T11:10:36.615129Z

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Observation dd9a29b6-8a1e-4d51-b50d-1b9bae1b2287 · outbound

This paper cites Sharp non-uniqueness for the Navier-Stokes equations in R^3.

Non-uniqueness of (Stochastic) Lagrangian Trajectories for Euler Equations Sharp non-uniqueness for the Navier-Stokes equations in R^3

Reference 41

Resolution: unresolved; no resolver link, observed 2026-08-16T11:10:36.620612Z

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Observation d98191f0-9ae8-48dc-b564-0077ebeec550 · outbound

This paper cites an unresolved cited work.

Non-uniqueness of (Stochastic) Lagrangian Trajectories for Euler Equations Unresolved cited work

Reference 42

Resolution: unresolved; raw_fallback, observed 2026-08-16T11:10:37.329229Z

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No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 98dae749-9233-4422-89cb-f7ef581b9507 · outbound

This paper cites Hofmanov´ a, R.

Non-uniqueness of (Stochastic) Lagrangian Trajectories for Euler Equations Hofmanov´ a, R

Reference 46

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T11:10:37.427085Z

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Observation 81a6bb82-c6cd-44e1-9277-fb59f108ec70 · outbound

This paper cites Stroock, Lectures on stochastic analysis: dif usion theory, LMS Student Texts, 1987 76 HUAXIANG L ¨U, MICHAEL R ¨OCKNER, AND XIANGCHAN ZHU [TBM20] S.

Non-uniqueness of (Stochastic) Lagrangian Trajectories for Euler Equations Stroock, Lectures on stochastic analysis: dif usion theory, LMS Student Texts, 1987 76 HUAXIANG L ¨U, MICHAEL R ¨OCKNER, AND XIANGCHAN ZHU [TBM20] S

Reference 47

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T11:10:37.280911Z

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No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 14d4e6a4-3658-4132-a30c-60941217651e · outbound

This paper cites Y amazaki.

Non-uniqueness of (Stochastic) Lagrangian Trajectories for Euler Equations Y amazaki

Reference 48

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T11:10:37.264928Z

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No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 28c3f79d-28d5-41c1-8f7a-9b6c9ecd61b1 · outbound

This paper cites Stochastic Lagrangian Flows for SDEs with rough coefficients.

Non-uniqueness of (Stochastic) Lagrangian Trajectories for Euler Equations Stochastic Lagrangian Flows for SDEs with rough coefficients

Reference 50

Resolution: unresolved; no resolver link, observed 2026-08-16T11:10:36.665719Z

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Observation bad3c15b-ba56-469a-b01c-21462d9f4ccd · outbound

This paper cites Y ao and A.

Non-uniqueness of (Stochastic) Lagrangian Trajectories for Euler Equations Y ao and A

Reference 69

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T11:10:37.247765Z

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Observation 41628d23-2e5a-43a5-88d7-c086a3269898 · outbound

This paper cites an unresolved cited work.

Non-uniqueness of (Stochastic) Lagrangian Trajectories for Euler Equations Unresolved cited work

Reference 93

Resolution: unresolved; raw_fallback, observed 2026-08-16T11:10:37.296274Z

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Observation 42e69a6f-6df1-42f6-9c12-391b6f7ba2f7 · outbound

This paper cites Non-uniqueness of Leray--Hopf solutions for the $3D$ fractional Navier--Stokes equations perturbed by transport noise.

Non-uniqueness of (Stochastic) Lagrangian Trajectories for Euler Equations Non-uniqueness of Leray--Hopf solutions for the $3D$ fractional Navier--Stokes equations perturbed by transport noise

Reference 114

Resolution: verified exact; local_arxiv, observed 2026-08-16T11:10:36.813877Z

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No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 878b11e6-de1d-4dd2-b9e5-cbfd2fd82f97 · outbound

This paper cites De Lellis, H.

Non-uniqueness of (Stochastic) Lagrangian Trajectories for Euler Equations De Lellis, H

Reference 200

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T11:10:37.526138Z

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No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 5527451d-91a5-450c-bb00-ce557e7218c1 · outbound

This paper cites Modena, L.

Non-uniqueness of (Stochastic) Lagrangian Trajectories for Euler Equations Modena, L

Reference 671

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T11:10:37.345452Z

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No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation f1457b2f-86b5-4ba3-82e4-80392c44cd64 · outbound

This paper cites Pitcho, M Sorella.

Non-uniqueness of (Stochastic) Lagrangian Trajectories for Euler Equations Pitcho, M Sorella

Reference 1804

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T11:10:37.311793Z

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No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation d4e43166-1464-49a8-a44c-8cb1dad14613 · outbound

This paper cites On measure-preserving selection of solutions of ODEs.

Non-uniqueness of (Stochastic) Lagrangian Trajectories for Euler Equations On measure-preserving selection of solutions of ODEs

Reference 1949

Resolution: verified exact; local_arxiv, observed 2026-08-16T11:10:36.756126Z

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No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 182786e5-b5b3-49e4-9057-72c589cf8362 · outbound

This paper cites Crippa, N.

Non-uniqueness of (Stochastic) Lagrangian Trajectories for Euler Equations Crippa, N

Reference 1994

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T11:10:37.573708Z

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Observation bd493516-6ff2-46b7-9562-5a33be0fda85 · outbound

This paper cites Compactly supported anomalous weak solutions for 2D Euler equations with vorticity in Hardy spaces.

Non-uniqueness of (Stochastic) Lagrangian Trajectories for Euler Equations Compactly supported anomalous weak solutions for 2D Euler equations with vorticity in Hardy spaces

Reference 1997

Resolution: unresolved; no resolver link, observed 2026-08-16T11:10:36.450030Z

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Observation 38908efd-bd86-4f99-a757-7a3d8d3bc824 · outbound

This paper cites SDEs with supercritical distributional drifts.

Non-uniqueness of (Stochastic) Lagrangian Trajectories for Euler Equations SDEs with supercritical distributional drifts

Reference 2002

Resolution: unresolved; no resolver link, observed 2026-08-16T11:10:36.547317Z

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Observation 420af312-cfac-4b63-acba-550d577e3c67 · outbound

This paper cites an unresolved cited work.

Non-uniqueness of (Stochastic) Lagrangian Trajectories for Euler Equations Unresolved cited work

Reference 2003

Resolution: unresolved; raw_fallback, observed 2026-08-16T11:10:37.360364Z

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Observation 6cdf5ba7-64fe-4752-a18f-81a03650d119 · outbound

This paper cites SDEs with critical time dependent drifts: strong solutions.

Non-uniqueness of (Stochastic) Lagrangian Trajectories for Euler Equations SDEs with critical time dependent drifts: strong solutions

Reference 2009

Resolution: unresolved; no resolver link, observed 2026-08-16T11:10:36.646129Z

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Observation 6470d81c-f2d2-471c-8714-b4276c4caa13 · outbound

This paper cites De Lellis and L.

Non-uniqueness of (Stochastic) Lagrangian Trajectories for Euler Equations De Lellis and L

Reference 2013

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T11:10:37.509864Z

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No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 4bebde8a-9ad3-42cd-8854-b2559e8be77a · outbound

This paper cites [BDLSV19] T.

Non-uniqueness of (Stochastic) Lagrangian Trajectories for Euler Equations [BDLSV19] T

Reference 2016

Resolution: malformed identifier; no resolver link, observed 2026-08-16T11:10:36.433217Z

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Observation 8049cac2-170c-4a0c-82cd-ac807dbf060f · outbound

This paper cites an unresolved cited work.

Non-uniqueness of (Stochastic) Lagrangian Trajectories for Euler Equations Unresolved cited work

Reference 2017

Resolution: unresolved; raw_fallback, observed 2026-08-16T11:10:37.621457Z

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Observation 3fe12bfb-13b8-4f89-9c05-cefdae28f626 · outbound

This paper cites an unresolved cited work.

Non-uniqueness of (Stochastic) Lagrangian Trajectories for Euler Equations Unresolved cited work

Reference 2018

Resolution: unresolved; no resolver link, observed 2026-08-16T11:10:36.563749Z

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Observation ee806820-fc22-4d71-8549-3a06057100d8 · outbound

This paper cites Ambrosio.

Non-uniqueness of (Stochastic) Lagrangian Trajectories for Euler Equations Ambrosio

Reference 2019

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T11:10:37.637444Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation f34aaf79-c4e2-4a64-a4b4-01ce08e6a94e · outbound

This paper cites Convex integration above the Onsager exponent for the forced Euler equations.

Non-uniqueness of (Stochastic) Lagrangian Trajectories for Euler Equations Convex integration above the Onsager exponent for the forced Euler equations

Reference 2020

Resolution: unresolved; no resolver link, observed 2026-08-16T11:10:36.439551Z

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Unavailable: canonical work link unavailable.

Observation 581a8dc9-a576-4f1e-956b-bfd5ca700c69 · outbound

This paper cites Caravenna, G.

Non-uniqueness of (Stochastic) Lagrangian Trajectories for Euler Equations Caravenna, G

Reference 2021

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T11:10:37.590369Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 8b9badd9-5def-4ada-9554-7807d721ba23 · outbound

This paper cites Extreme temporal intermittency in the linear Sobolev transport: almost smooth nonunique solutions.

Non-uniqueness of (Stochastic) Lagrangian Trajectories for Euler Equations Extreme temporal intermittency in the linear Sobolev transport: almost smooth nonunique solutions

Reference 2022

Resolution: verified exact; local_arxiv, observed 2026-08-16T11:10:37.091421Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 209afead-a1d1-4528-9c8f-549516b619a8 · outbound

This paper cites Sharp Nonuniqueness in the Transport Equation with Sobolev Velocity Field.

Non-uniqueness of (Stochastic) Lagrangian Trajectories for Euler Equations Sharp Nonuniqueness in the Transport Equation with Sobolev Velocity Field

Reference 2023

Resolution: unresolved; no resolver link, observed 2026-08-16T11:10:36.414981Z

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Unavailable: canonical work link unavailable.

Observation 6577bcfe-9233-45f4-95d0-f98e10d4370e · outbound

This paper cites Flexibility of Two-Dimensional Euler Flows with Integrable Vorticity.

Non-uniqueness of (Stochastic) Lagrangian Trajectories for Euler Equations Flexibility of Two-Dimensional Euler Flows with Integrable Vorticity

Reference 2024

Resolution: unresolved; no resolver link, observed 2026-08-16T11:10:36.421403Z

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Observation 32ef9863-3fbf-4555-929f-d1021dc3d4b1 · outbound

This paper cites an unresolved cited work.

Non-uniqueness of (Stochastic) Lagrangian Trajectories for Euler Equations Unresolved cited work

Reference 2025

Resolution: unresolved; raw_fallback, observed 2026-08-16T11:10:37.541417Z

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No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Pith citing papers

Observation c847f88d-f893-4097-8dcf-bd5d9bba93ea · inbound

Non-Uniqueness for Nonlinear Fokker--Planck Equations and Their Associated Distribution-Dependent SDEs cites this paper.

Non-Uniqueness for Nonlinear Fokker--Planck Equations and Their Associated Distribution-Dependent SDEs Non-uniqueness of (Stochastic) Lagrangian Trajectories for Euler Equations

Reference 21

Resolution: verified exact; arxiv_id, observed 2026-07-01T11:35:43.514128Z

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No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.