Stability of Navier-Stokes-Oseen flows

Duoc Viet Trinh; Duoc Viet Trinh

doi:10.3934/cam.2025036

Communications in Analysis and Mechanics

2025, Volume 17, Issue 4: 898-909. doi: 10.3934/cam.2025036

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Research article

Stability of Navier-Stokes-Oseen flows

Duoc Viet Trinh ^{1,2
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1.
Faculty of Mathematics, Mechanics, and Informatics, University of Science, Vietnam National University, 334 Nguyen Trai, Hanoi, Vietnam
2.
Thang Long Institute of Mathematics and Applied Sciences, Thang Long University, Nghiem Xuan Yem, Hanoi, Vietnam

Received: 30 October 2024 Revised: 10 February 2025 Accepted: 29 August 2025 Published: 29 October 2025
35B35, 35Q30, 35Q35, 76D07

This paper studies the stability of a weak mild solution of the Navier–Stokes–Oseen equations in the solenoidal Lorentz space $ L^{3}_{\sigma, {{{\rm{w}}}}} $. 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.
- stability,
- Navier–Stokes–Oseen equations,
- Oseen operator,
- rotating and translating obstacle,
- solenoidal Lorentz spaces
Citation: Duoc Viet Trinh. Stability of Navier-Stokes-Oseen flows[J]. Communications in Analysis and Mechanics, 2025, 17(4): 898-909. doi: 10.3934/cam.2025036

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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^{3}_{\sigma, {{{\rm{w}}}}} $. 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.

References

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