A note on 2D Navier-Stokes system in a bounded domain

Jishan Fan; Tohru Ozawa; Jishan Fan; Tohru Ozawa

doi:10.3934/math.20241213

AIMS Mathematics

2024, Volume 9, Issue 9: 24908-24911. doi: 10.3934/math.20241213

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Research article

A note on 2D Navier-Stokes system in a bounded domain

Jishan Fan ¹,
Tohru Ozawa ^{2
,
,}

1.
Department of Applied Mathematics, Nanjing Forestry University, Nanjing 210037, China
2.
Department of Applied Physics, Waseda University, Tokyo, 169-8555, Japan

Received: 05 July 2024 Revised: 13 August 2024 Accepted: 14 August 2024 Published: 26 August 2024
MSC : 35Q30, 76D03, 76D05

This paper poses a new question and proves a related result. Particularly, the nonexistence of a nontrivial time-periodic solution to the Navier–Stokes system is proved in a bounded domain in $ \mathbb{R}^2 $.
- time-periodic,
- 2D Navier–Stokes flow,
- open problem,
- stationary solution,
- vector Poincaré inequality
Citation: Jishan Fan, Tohru Ozawa. A note on 2D Navier-Stokes system in a bounded domain[J]. AIMS Mathematics, 2024, 9(9): 24908-24911. doi: 10.3934/math.20241213

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Abstract

This paper poses a new question and proves a related result. Particularly, the nonexistence of a nontrivial time-periodic solution to the Navier–Stokes system is proved in a bounded domain in $ \mathbb{R}^2 $.

References

[1]	L. C. Berselli, M. Romito, On the existence and uniqueness of weak solutions for a vorticity seeding model, SIAM J. Math. Anal., 37 (2006), 1780–1799. https://doi.org/10.1137/04061249X doi: 10.1137/04061249X
[2]	T. Qi, On an evolutionary system of Ginzburg-Landau equations with fixed total magnetic flux, Commun. Part. Diff. Eq., 20 (1995), 1–36. https://doi.org/10.1080/03605309508821085 doi: 10.1080/03605309508821085
[3]	J. Fan, T. Ozawa, Long time behavior of a 2D Ginzburg-Landau model with fixed total magnetic flux, International Journal of Mathematical Analysis, 17 (2023), 109–117. https://doi.org/10.12988/ijma.2023.912516 doi: 10.12988/ijma.2023.912516
[4]	P. L. Lions, Mathematical topics in fluid mechanics: Volume 2: compressible models, New York: Oxford University Press, 1998.

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