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Research Article | Open Access

Stability of Navier-Stokes-Oseen flows

Faculty of Mathematics, Mechanics, and Informatics, University of Science, Vietnam National University, 334 Nguyen Trai, Hanoi, Vietnam
Thang Long Institute of Mathematics and Applied Sciences, Thang Long University, Nghiem Xuan Yem, Hanoi, Vietnam
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Abstract

This paper studies the stability of a weak mild solution of the Navier–Stokes–Oseen equations in the solenoidal Lorentz space L σ , w 3 . Our approach relies on dual space pair and suitable estimates in our setting for the Oseen semigroup. Therefore, we get a new result for the stability of a weak mild solution following the initial datum and external force.

Keywords

stabilityNavier–Stokes–Oseen equationsOseen operatorrotating and translating obstaclesolenoidal Lorentz spaces
CLC number: 35B35, 35Q30, 35Q35, 76D07

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Communications in Analysis and Mechanics
Volume 17 Issue 4,
December 2025
Pages 898-909
DOI: 10.3934/cam.2025036

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Cite this article:
Trinh DV. Stability of Navier-Stokes-Oseen flows. Communications in Analysis and Mechanics, 2025, 17(4): 898-909. https://doi.org/10.3934/cam.2025036

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Received: 30 October 2024
Revised: 10 February 2025
Accepted: 29 August 2025
Published: 15 December 2025
©2025 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)