Paper Citation Record · LEDGER

Inhomogeneous 2D Navier--Stokes equations: Existence, uniqueness, stability, continuity in time and energy conservation of weak solutions

As of 16 August 2026, this Paper Citation Record lists 35 of 35 outbound references and 2 inbound Pith citation observations for arXiv:2504.16638.

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pith.paper-citation-record.v1
2504.16638 v2

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measured 35 of 35 reference resolution

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Source: paper_references, paper_reference_links, observed 2026-08-16T11:08:44.864666Z

measured 37 of 37 standing notices

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measured 2 of 2 inbound itemization

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Source: paper_references, paper_reference_links, observed 2026-07-14T10:03:03.189441Z

measured 0 of 1 external citation measurements

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Source: arxiv_reference, observed 2026-05-10T09:08:26.212235Z

Reference resolution

35 of 35 outbound references displayed

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verified fuzzy8
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Outbound references

Observation ad554899-e43f-4d87-9a78-4bdb09b660ed · outbound

This paper cites Navier-Stokes equation with variable d ensity and viscosity in critical space.

Inhomogeneous 2D Navier--Stokes equations: Existence, uniqueness, stability, continuity in time and energy conservation of weak solutions Navier-Stokes equation with variable d ensity and viscosity in critical space

Reference 1

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Observation b7f3742c-be1f-472c-8c58-f0fffba955ff · outbound

This paper cites Global well-posedness f or the 2 -D inhomogeneous incom- pressible Navier-Stokes system with large initial data in c ritical spaces.

Inhomogeneous 2D Navier--Stokes equations: Existence, uniqueness, stability, continuity in time and energy conservation of weak solutions Global well-posedness f or the 2 -D inhomogeneous incom- pressible Navier-Stokes system with large initial data in c ritical spaces

Reference 2

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Observation 5b1cb696-cd3b-4996-b77d-324db1f9464e · outbound

This paper cites On the globa l existence and uniqueness of so- lution to 2-D inhomogeneous incompressible Navier-Stokes equations in critical spaces.

Inhomogeneous 2D Navier--Stokes equations: Existence, uniqueness, stability, continuity in time and energy conservation of weak solutions On the globa l existence and uniqueness of so- lution to 2-D inhomogeneous incompressible Navier-Stokes equations in critical spaces

Reference 3

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Observation 042fbbb2-d875-4d8b-8f57-6450e6f00985 · outbound

This paper cites Inhomogenous Navier--Stokes equations with unbounded density.

Inhomogeneous 2D Navier--Stokes equations: Existence, uniqueness, stability, continuity in time and energy conservation of weak solutions Inhomogenous Navier--Stokes equations with unbounded density

Reference 4

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Observation 9d9f2f15-a8c9-49e9-93e3-357458b272f3 · outbound

This paper cites Continuity equati ons and ODE ﬂows with non-smooth velocity.

Inhomogeneous 2D Navier--Stokes equations: Existence, uniqueness, stability, continuity in time and energy conservation of weak solutions Continuity equati ons and ODE ﬂows with non-smooth velocity

Reference 5

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Observation 788c0ea6-ba2b-4274-a484-a6c708a1d00d · outbound

This paper cites Fourier analysis and nonlinear par- tial diﬀerential equations.

Inhomogeneous 2D Navier--Stokes equations: Existence, uniqueness, stability, continuity in time and energy conservation of weak solutions Fourier analysis and nonlinear par- tial diﬀerential equations

Reference 6

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Observation 99efd76d-3102-4946-8008-689f1adb7f31 · outbound

This paper cites Fujita- Kato theorem for the 3-D inhomo- geneous Navier-Stokes equations.

Inhomogeneous 2D Navier--Stokes equations: Existence, uniqueness, stability, continuity in time and energy conservation of weak solutions Fujita- Kato theorem for the 3-D inhomo- geneous Navier-Stokes equations

Reference 7

Resolution: verified exact; doi, observed 2026-08-16T11:08:45.588177Z

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Observation 73cf918a-487c-4f9c-9c1c-f9e311da5133 · outbound

This paper cites Regularity aspects of Leray-Hopf solutions to the 2D Inhomogeneous Navier-Stokes system and applications to weak-strong uniqueness.

Inhomogeneous 2D Navier--Stokes equations: Existence, uniqueness, stability, continuity in time and energy conservation of weak solutions Regularity aspects of Leray-Hopf solutions to the 2D Inhomogeneous Navier-Stokes system and applications to weak-strong uniqueness

Reference 8

Resolution: verified exact; local_arxiv, observed 2026-08-16T11:08:46.233653Z

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Observation e3dc5f3c-54bf-4aaa-9570-37d14decc7a9 · outbound

This paper cites Relative energy method for weak–strong uniqueness of the inhomogeneous Navier–Stoke s equations far from vacuum.

Inhomogeneous 2D Navier--Stokes equations: Existence, uniqueness, stability, continuity in time and energy conservation of weak solutions Relative energy method for weak–strong uniqueness of the inhomogeneous Navier–Stoke s equations far from vacuum

Reference 9

Resolution: verified exact; doi, observed 2026-08-16T11:08:45.499592Z

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Observation 780c441d-b135-4872-9124-053566117f48 · outbound

This paper cites The ﬂow associated to weakly diﬀeren tiable vector ﬁelds.

Inhomogeneous 2D Navier--Stokes equations: Existence, uniqueness, stability, continuity in time and energy conservation of weak solutions The ﬂow associated to weakly diﬀeren tiable vector ﬁelds

Reference 10

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Observation 7d731baf-78e4-4104-8ba1-5cebf87f98df · outbound

This paper cites Density-dependent indecompressible vis cous ﬂuids in critical spaces.

Inhomogeneous 2D Navier--Stokes equations: Existence, uniqueness, stability, continuity in time and energy conservation of weak solutions Density-dependent indecompressible vis cous ﬂuids in critical spaces

Reference 11

Resolution: verified exact; doi, observed 2026-08-16T11:08:45.430979Z

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Observation 974e61c3-6e90-4fc4-9842-f2bb37cfda6b · outbound

This paper cites Local and global well-posedness results f or ﬂows of inhomogeneous viscous ﬂuids.

Inhomogeneous 2D Navier--Stokes equations: Existence, uniqueness, stability, continuity in time and energy conservation of weak solutions Local and global well-posedness results f or ﬂows of inhomogeneous viscous ﬂuids

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T11:08:46.652514Z

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Observation 649ec19c-98e9-4403-8da8-d7b623fc066d · outbound

This paper cites Global well-posedness for 2D inhomo geneous viscous ﬂows with rough data via dynamic interpolation.

Inhomogeneous 2D Navier--Stokes equations: Existence, uniqueness, stability, continuity in time and energy conservation of weak solutions Global well-posedness for 2D inhomo geneous viscous ﬂows with rough data via dynamic interpolation

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T11:08:46.640712Z

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Observation 78aa9bf0-8e2f-4af2-9f53-5db751116976 · outbound

This paper cites Incompress ible ﬂows with piecewise constant density.

Inhomogeneous 2D Navier--Stokes equations: Existence, uniqueness, stability, continuity in time and energy conservation of weak solutions Incompress ible ﬂows with piecewise constant density

Reference 14

Resolution: verified exact; doi, observed 2026-08-16T11:08:45.343811Z

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Observation 3174f0be-770f-4abe-bc7a-adf842f035d6 · outbound

This paper cites A Lagrangia n approach for the incompressible Navier-Stokes equations with variable density.

Inhomogeneous 2D Navier--Stokes equations: Existence, uniqueness, stability, continuity in time and energy conservation of weak solutions A Lagrangia n approach for the incompressible Navier-Stokes equations with variable density

Reference 15

Resolution: verified exact; doi, observed 2026-08-16T11:08:45.333262Z

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Observation 89ca5433-c328-477e-a38c-635a2f821630 · outbound

This paper cites The incompr essible Navier-Stokes equations in vacuum.

Inhomogeneous 2D Navier--Stokes equations: Existence, uniqueness, stability, continuity in time and energy conservation of weak solutions The incompr essible Navier-Stokes equations in vacuum

Reference 16

Resolution: verified exact; doi, observed 2026-08-16T11:08:45.265556Z

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Observation 6f21d6e6-67fb-4c85-adec-9ff2ee06c5b6 · outbound

This paper cites Global unique solution s for the inhomogeneous Navier- Stokes equations with only bounded density, in critical reg ularity spaces.

Inhomogeneous 2D Navier--Stokes equations: Existence, uniqueness, stability, continuity in time and energy conservation of weak solutions Global unique solution s for the inhomogeneous Navier- Stokes equations with only bounded density, in critical reg ularity spaces

Reference 17

Resolution: verified exact; doi, observed 2026-08-16T11:08:45.254282Z

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Observation 300634e7-3b86-4574-8786-691d9ef84556 · outbound

This paper cites Linear transport equations with i nitial values in Sobolev spaces and ap- plication to the Navier-Stokes equations.

Inhomogeneous 2D Navier--Stokes equations: Existence, uniqueness, stability, continuity in time and energy conservation of weak solutions Linear transport equations with i nitial values in Sobolev spaces and ap- plication to the Navier-Stokes equations

Reference 18

Resolution: verified exact; raw_fallback, observed 2026-08-16T11:08:46.217657Z

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Observation e5d9d66a-9b59-4ef2-aa30-28bed4fb5510 · outbound

This paper cites Ordinary diﬀerential eq uations, transport theory and Sobolev spaces.

Inhomogeneous 2D Navier--Stokes equations: Existence, uniqueness, stability, continuity in time and energy conservation of weak solutions Ordinary diﬀerential eq uations, transport theory and Sobolev spaces

Reference 19

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Observation a442004b-942c-491f-b428-66de7ec182a0 · outbound

This paper cites Global well-posedness of inhomogeneous Navier-Stokes equations with bounded density.

Inhomogeneous 2D Navier--Stokes equations: Existence, uniqueness, stability, continuity in time and energy conservation of weak solutions Global well-posedness of inhomogeneous Navier-Stokes equations with bounded density

Reference 20

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Observation f2c138b6-24b9-45fa-b478-16ea3da6c998 · outbound

This paper cites Solvability of theinitial and boundary -value problem for the equations of motions of an inhomogeneous viscous incompressible ﬂuid.

Inhomogeneous 2D Navier--Stokes equations: Existence, uniqueness, stability, continuity in time and energy conservation of weak solutions Solvability of theinitial and boundary -value problem for the equations of motions of an inhomogeneous viscous incompressible ﬂuid

Reference 22

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Observation 99db19da-f05f-41ec-9723-6f2fbbb73e61 · outbound

This paper cites The unique sol vability of an initial-boundary value problem for viscous incompressible inhomogeneous ﬂuids.

Inhomogeneous 2D Navier--Stokes equations: Existence, uniqueness, stability, continuity in time and energy conservation of weak solutions The unique sol vability of an initial-boundary value problem for viscous incompressible inhomogeneous ﬂuids

Reference 23

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Observation 8e670735-2ee7-415c-b2c4-7ffadc6c5539 · outbound

This paper cites Solution “in the large.

Inhomogeneous 2D Navier--Stokes equations: Existence, uniqueness, stability, continuity in time and energy conservation of weak solutions Solution “in the large

Reference 24

Resolution: verified exact; doi, observed 2026-08-16T11:08:45.172929Z

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Observation f84c4236-2568-4fcc-8e99-db105ffc51f9 · outbound

This paper cites On the movement of a space-ﬁlling viscous l iquid.

Inhomogeneous 2D Navier--Stokes equations: Existence, uniqueness, stability, continuity in time and energy conservation of weak solutions On the movement of a space-ﬁlling viscous l iquid

Reference 25

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Observation f8e1018f-5d8b-4c7f-b88a-b0c418fddf6f · outbound

This paper cites Un théorème d ’existence et unicité dans les équa- tions de Navier- Stokes en dimension 2.

Inhomogeneous 2D Navier--Stokes equations: Existence, uniqueness, stability, continuity in time and energy conservation of weak solutions Un théorème d ’existence et unicité dans les équa- tions de Navier- Stokes en dimension 2

Reference 26

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T11:08:46.471921Z

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Observation 125f0eb9-3305-4a36-95da-bbd2b2e6f183 · outbound

This paper cites Mathematical topics in ﬂuid mechanics.

Inhomogeneous 2D Navier--Stokes equations: Existence, uniqueness, stability, continuity in time and energy conservation of weak solutions Mathematical topics in ﬂuid mechanics

Reference 27

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T11:08:46.405186Z

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Observation ad6592b5-08a3-496f-a6e3-989ad2280c1e · outbound

This paper cites WEAK SOLUTIONS OF NA VIER-STOKES EQUATIONS.

Inhomogeneous 2D Navier--Stokes equations: Existence, uniqueness, stability, continuity in time and energy conservation of weak solutions WEAK SOLUTIONS OF NA VIER-STOKES EQUATIONS

Reference 28

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T11:08:46.350936Z

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Observation 6fa9bcd9-113f-4901-9f0e-96799958b84c · outbound

This paper cites Global uni que solvability of inhomogeneous Navier-Stokes equations with bounded density.

Inhomogeneous 2D Navier--Stokes equations: Existence, uniqueness, stability, continuity in time and energy conservation of weak solutions Global uni que solvability of inhomogeneous Navier-Stokes equations with bounded density

Reference 29

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Observation 1d6e2255-42d7-400d-b16f-47c1a9c23e83 · outbound

This paper cites Free boundary regularity of vacuum states for incompressible viscous flows in unbounded domains.

Inhomogeneous 2D Navier--Stokes equations: Existence, uniqueness, stability, continuity in time and energy conservation of weak solutions Free boundary regularity of vacuum states for incompressible viscous flows in unbounded domains

Reference 30

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Observation 6790065c-f9e2-40a5-b28c-ae819797377f · outbound

This paper cites Nonhomogeneous viscous incompressib le ﬂuids: existence of velocity, density, and pressure.

Inhomogeneous 2D Navier--Stokes equations: Existence, uniqueness, stability, continuity in time and energy conservation of weak solutions Nonhomogeneous viscous incompressib le ﬂuids: existence of velocity, density, and pressure

Reference 31

Resolution: verified exact; doi, observed 2026-08-16T11:08:45.088360Z

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Observation 7e8c34e6-a917-45be-9536-d7a8e0245dbd · outbound

This paper cites Weak-strong uniqueness in ﬂuid dynam ics.

Inhomogeneous 2D Navier--Stokes equations: Existence, uniqueness, stability, continuity in time and energy conservation of weak solutions Weak-strong uniqueness in ﬂuid dynam ics

Reference 32

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T11:08:46.336547Z

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Observation abbf3edc-77ad-4e86-8775-4263d4e388de · outbound

This paper cites Maximal L1 regularity for solutions to inhomogeneous incompressible Navier- Stokes equations.

Inhomogeneous 2D Navier--Stokes equations: Existence, uniqueness, stability, continuity in time and energy conservation of weak solutions Maximal L1 regularity for solutions to inhomogeneous incompressible Navier- Stokes equations

Reference 33

Resolution: verified exact; doi, observed 2026-08-16T11:08:44.946238Z

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No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation d6abe229-57f1-4baa-9f47-0793f242a32f · outbound

This paper cites Global Fujita-Kato solution of 3-d inhomo geneous incompressible Navier-Stokes system.

Inhomogeneous 2D Navier--Stokes equations: Existence, uniqueness, stability, continuity in time and energy conservation of weak solutions Global Fujita-Kato solution of 3-d inhomo geneous incompressible Navier-Stokes system

Reference 34

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Observation 6631ef96-91f5-474c-9eee-a89fc084d16b · outbound

This paper cites doi: 10.1017/9781108610575.012.

Inhomogeneous 2D Navier--Stokes equations: Existence, uniqueness, stability, continuity in time and energy conservation of weak solutions doi: 10.1017/9781108610575.012

Reference 326

Resolution: verified exact; doi, observed 2026-08-16T11:08:44.992797Z

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Observation b4e16e12-ffd7-4373-a0a2-ff8e0820fac8 · outbound

This paper cites On the density patch problem for the 2-D inhomogeneous Navier-Stokes equations.

Inhomogeneous 2D Navier--Stokes equations: Existence, uniqueness, stability, continuity in time and energy conservation of weak solutions On the density patch problem for the 2-D inhomogeneous Navier-Stokes equations

Reference 2024

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Pith citing papers

Observation 972667e7-ee5a-43a6-af51-2991a2546823 · inbound

On Lions' density patch problem at a critical level of regularity cites this paper.

On Lions' density patch problem at a critical level of regularity Inhomogeneous 2D Navier--Stokes equations: Existence, uniqueness, stability, continuity in time and energy conservation of weak solutions

Reference 32

Resolution: verified exact; arxiv_id, observed 2026-07-28T01:22:19.721608Z

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Observation fbb9b088-d1f2-4801-8b99-eda1bdafeb1a · inbound

$L^2(\mathbb{R}^2)$ Well-Posedness and Logarithmic Lipschitz Regularity for the Density Patch Problem cites this paper.

$L^2(\mathbb{R}^2)$ Well-Posedness and Logarithmic Lipschitz Regularity for the Density Patch Problem Inhomogeneous 2D Navier--Stokes equations: Existence, uniqueness, stability, continuity in time and energy conservation of weak solutions

Reference 24

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