Paper Citation Record · LEDGER

Exponential decay for the 3D Boussinesq equations with Navier boundary conditions

As of 11 August 2026, this Paper Citation Record lists 25 of 25 outbound references and 0 inbound Pith citation observations for arXiv:2608.00972.

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pith.paper-citation-record.v1
2608.00972 v1

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measured 25 of 25 reference resolution

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Source: paper_references, paper_reference_links, observed 2026-08-06T00:54:57.882338Z

measured 25 of 25 standing notices

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Source: scholarly_work_events, retraction_status_cache, observed 2026-08-11T06:34:44.6726+00:00

measured 0 of 0 inbound itemization

Pith citing papers itemized under the disclosed page cap.

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measured 0 of 1 external citation measurements

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Source: cited_works

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25 of 25 outbound references displayed

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Outbound references

Observation a9b90abc-4cc0-453a-aa74-266440d09a5c · outbound

This paper cites Large-time behavior of the 2D thermally non- diffusive Boussinesq equations with Navier-slip boundary conditions.Zeitschrift f¨ ur Angewandte Math- ematik und Physik, 76:58, 2025.

Exponential decay for the 3D Boussinesq equations with Navier boundary conditions Large-time behavior of the 2D thermally non- diffusive Boussinesq equations with Navier-slip boundary conditions.Zeitschrift f¨ ur Angewandte Math- ematik und Physik, 76:58, 2025

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T00:55:58.805700Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation fcc92147-4040-491c-bc1f-f1d1efb13bf2 · outbound

This paper cites Stability and enhanced decay rate for 3D anisotropic Boussinesq equations near the hydrostatic balance.Journal of Differential Equations, 425:300–341, 2025.

Exponential decay for the 3D Boussinesq equations with Navier boundary conditions Stability and enhanced decay rate for 3D anisotropic Boussinesq equations near the hydrostatic balance.Journal of Differential Equations, 425:300–341, 2025

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T00:55:58.647741Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation df0380bb-4e19-49ba-88bf-c7d810e5bd5e · outbound

This paper cites Global existence and Rayleigh-Taylor instability for the semi-dissipative Boussinesq system with Naiver boundary conditions.

Exponential decay for the 3D Boussinesq equations with Navier boundary conditions Global existence and Rayleigh-Taylor instability for the semi-dissipative Boussinesq system with Naiver boundary conditions

Reference 3

Resolution: verified exact; local_arxiv, observed 2026-08-06T00:54:58.247385Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 7a5c4fd9-5bef-401d-98f7-c19ec3985b60 · outbound

This paper cites The optimal decay rates for solutions to the 3D Boussinesq equations with a velocity damping term inR 3.Nonlinear Analysis, 255:113775, 2025.

Exponential decay for the 3D Boussinesq equations with Navier boundary conditions The optimal decay rates for solutions to the 3D Boussinesq equations with a velocity damping term inR 3.Nonlinear Analysis, 255:113775, 2025

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T00:55:58.500972Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 216b3e63-ab53-45ef-add3-60c21fe982de · outbound

This paper cites On asymptotic stability of the 3D Boussinesq equations without heat conduction.Science China Mathematics, 67(2):253–280, 2024.

Exponential decay for the 3D Boussinesq equations with Navier boundary conditions On asymptotic stability of the 3D Boussinesq equations without heat conduction.Science China Mathematics, 67(2):253–280, 2024

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T00:55:58.333380Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 6334ebae-c99f-4824-997b-ea72ae52304e · outbound

This paper cites The 2D Boussinesq–Navier–Stokes equations with logarithmically supercritical dissipation.Journal of Mathematical Study, 57(1):101–132, 2024.

Exponential decay for the 3D Boussinesq equations with Navier boundary conditions The 2D Boussinesq–Navier–Stokes equations with logarithmically supercritical dissipation.Journal of Mathematical Study, 57(1):101–132, 2024

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T00:55:58.146454Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 67a8424a-3b50-49e0-93d4-1d6242b1891e · outbound

This paper cites Nonlinear Rayleigh–Taylor instability of inho- mogeneous incompressible geophysical fluids with partial dissipation.Nonlinearity, 38(5):055016, 2025.

Exponential decay for the 3D Boussinesq equations with Navier boundary conditions Nonlinear Rayleigh–Taylor instability of inho- mogeneous incompressible geophysical fluids with partial dissipation.Nonlinearity, 38(5):055016, 2025

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T00:55:58.001637Z

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No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 57dee645-8a2f-4401-a19e-98692bbc4574 · outbound

This paper cites Partially dissipative 2D Boussinesq equations with Navier type boundary conditions.Physica D: Nonlinear Phenomena, 376:39–48, 2018.

Exponential decay for the 3D Boussinesq equations with Navier boundary conditions Partially dissipative 2D Boussinesq equations with Navier type boundary conditions.Physica D: Nonlinear Phenomena, 376:39–48, 2018

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T00:55:57.798756Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 8db06d69-0d61-4e55-9e63-60fa4cf6d192 · outbound

This paper cites Uniqueness of weak solutions to the Boussinesq equations with fractional dissipation.Communications in Mathematical Sciences, 21(6):1531–1548, 2023.

Exponential decay for the 3D Boussinesq equations with Navier boundary conditions Uniqueness of weak solutions to the Boussinesq equations with fractional dissipation.Communications in Mathematical Sciences, 21(6):1531–1548, 2023

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T00:55:57.612423Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 879681cf-bef8-4d27-8bdc-966354b4f890 · outbound

This paper cites Kelliher, Christophe Lacave, Milton C.

Exponential decay for the 3D Boussinesq equations with Navier boundary conditions Kelliher, Christophe Lacave, Milton C

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T00:55:57.399828Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 75563835-c8e3-4cf9-9b02-6f96d98ec252 · outbound

This paper cites Global Sobolev persistence for the fractional Boussinesq equations with zero diffusivity.Pure and Applied Functional Analysis, 5(1):27–45, 2020.

Exponential decay for the 3D Boussinesq equations with Navier boundary conditions Global Sobolev persistence for the fractional Boussinesq equations with zero diffusivity.Pure and Applied Functional Analysis, 5(1):27–45, 2020

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T00:55:57.213375Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation e0462b9b-03ef-48a3-9370-a28c376e55be · outbound

This paper cites Long time behavior of solutions to the 2D Boussinesq equations with zero diffusivity.Journal of Dynamics and Differential Equations, 32(4):2061–2077, 2020.

Exponential decay for the 3D Boussinesq equations with Navier boundary conditions Long time behavior of solutions to the 2D Boussinesq equations with zero diffusivity.Journal of Dynamics and Differential Equations, 32(4):2061–2077, 2020

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T00:55:57.053025Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation c3a7d4d0-0529-401e-b705-a96ea03f124c · outbound

This paper cites Stability and large-time behavior of the 2D Boussinesq equations with partial dissipation.Journal of Differential Equations, 271:764–796, 2021.

Exponential decay for the 3D Boussinesq equations with Navier boundary conditions Stability and large-time behavior of the 2D Boussinesq equations with partial dissipation.Journal of Differential Equations, 271:764–796, 2021

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T00:55:56.880675Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 19634681-876f-4da9-a3a3-8ab9ef5656fa · outbound

This paper cites Norm inflation for the Boussinesq system.Discrete and Continuous Dynamical Systems – Series B, 26(10):5449–5463, 2021.

Exponential decay for the 3D Boussinesq equations with Navier boundary conditions Norm inflation for the Boussinesq system.Discrete and Continuous Dynamical Systems – Series B, 26(10):5449–5463, 2021

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T00:55:56.727276Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 9309757c-74f2-4c29-87d2-1bfe0783e292 · outbound

This paper cites The stability and decay of 2D in- compressible Boussinesq equation with partial vertical dissipation.Communications in Analysis and Mechanics, 17(1):100–127, 2025.

Exponential decay for the 3D Boussinesq equations with Navier boundary conditions The stability and decay of 2D in- compressible Boussinesq equation with partial vertical dissipation.Communications in Analysis and Mechanics, 17(1):100–127, 2025

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T00:55:56.477697Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 686e9e64-ffb0-4570-abb3-de4754809f6e · outbound

This paper cites Stability of 3D perturbations near a special 2D solution to the rotating Boussinesq equations.Studies in Applied Mathematics, 148(4):1624–1655, 2022.

Exponential decay for the 3D Boussinesq equations with Navier boundary conditions Stability of 3D perturbations near a special 2D solution to the rotating Boussinesq equations.Studies in Applied Mathematics, 148(4):1624–1655, 2022

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T00:55:56.255847Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 5ddedb37-a6a2-4e4a-9292-7f72cc6ebfd5 · outbound

This paper cites M´ emoire sur les lois du mouvement des fluides.M´ emoires de l’Acad´ emie Royale des Sciences de l’Institut de France, 6:389–440, 1827.

Exponential decay for the 3D Boussinesq equations with Navier boundary conditions M´ emoire sur les lois du mouvement des fluides.M´ emoires de l’Acad´ emie Royale des Sciences de l’Institut de France, 6:389–440, 1827

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T00:55:56.062838Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 00d114b2-3298-4dd3-92ec-4febb97109cb · outbound

This paper cites an unresolved cited work.

Exponential decay for the 3D Boussinesq equations with Navier boundary conditions Unresolved cited work

Reference 18

Resolution: unresolved; raw_fallback, observed 2026-08-06T00:55:55.804160Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 349585d1-2010-4a96-a7c7-c3f6c795b30e · outbound

This paper cites A global regularity result for the 2D Boussinesq equations with critical dissipation.Journal d’Analyse Math´ ematique, 137(1):269–290, 2019.

Exponential decay for the 3D Boussinesq equations with Navier boundary conditions A global regularity result for the 2D Boussinesq equations with critical dissipation.Journal d’Analyse Math´ ematique, 137(1):269–290, 2019

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T00:55:55.566413Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation c431264b-496e-48f9-8ff4-512f257621e3 · outbound

This paper cites Global regularity results of the 2D fractional Boussinesq equations.Mathematische Annalen, 391(4):5965–6012, 2025.

Exponential decay for the 3D Boussinesq equations with Navier boundary conditions Global regularity results of the 2D fractional Boussinesq equations.Mathematische Annalen, 391(4):5965–6012, 2025

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T00:54:59.728027Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 7d508c42-3e84-47d0-8725-4967d19122ca · outbound

This paper cites On the global regularity for a 3D Boussinesq model without thermal diffusion.Zeitschrift f¨ ur Angewandte Mathematik und Physik, 70(6):174, 2019.

Exponential decay for the 3D Boussinesq equations with Navier boundary conditions On the global regularity for a 3D Boussinesq model without thermal diffusion.Zeitschrift f¨ ur Angewandte Mathematik und Physik, 70(6):174, 2019

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T00:54:59.590885Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 1ad98f69-211a-4d66-b174-a657c36092e2 · outbound

This paper cites On the global stability of large solutions for the Boussinesq equations with Navier boundary conditions.Archiv der Mathematik, 116(4):445–456, 2021.

Exponential decay for the 3D Boussinesq equations with Navier boundary conditions On the global stability of large solutions for the Boussinesq equations with Navier boundary conditions.Archiv der Mathematik, 116(4):445–456, 2021

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T00:54:59.383356Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 2a0af6fb-1850-4856-8daf-16783feb9a9a · outbound

This paper cites On 2D incompressible Boussinesq systems: global stabilization under dynamic boundary conditions.Journal of Differential Equations, 367:246–289, 2023.

Exponential decay for the 3D Boussinesq equations with Navier boundary conditions On 2D incompressible Boussinesq systems: global stabilization under dynamic boundary conditions.Journal of Differential Equations, 367:246–289, 2023

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T00:54:59.155288Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation e69e454b-3ef7-46d8-b988-251c7e090241 · outbound

This paper cites Well-posedness and exponential stability for Boussinesq sys- tems on real hyperbolic manifolds and application.Asymptotic Analysis, 148(3):803–824, 2026.

Exponential decay for the 3D Boussinesq equations with Navier boundary conditions Well-posedness and exponential stability for Boussinesq sys- tems on real hyperbolic manifolds and application.Asymptotic Analysis, 148(3):803–824, 2026

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T00:54:58.871862Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 4411f868-e959-40e8-9d53-861b56439d83 · outbound

This paper cites On certain classes of mild solutions for Boussinesq systems: a framework of curved spaces.Zeitschrift f¨ ur Angewandte Mathematik und Physik, 76(5):214, 2025.

Exponential decay for the 3D Boussinesq equations with Navier boundary conditions On certain classes of mild solutions for Boussinesq systems: a framework of curved spaces.Zeitschrift f¨ ur Angewandte Mathematik und Physik, 76(5):214, 2025

Reference 25

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T00:54:58.506786Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

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