| Autor: |
Ferriere, Guillaume, Hillairet, Matthieu |
| Jazyk: |
English<br />French |
| Rok vydání: |
2023 |
| Předmět: |
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| Zdroj: |
Comptes Rendus. Mathématique, Vol 361, Iss G2, Pp 453-485 (2023) |
| Druh dokumentu: |
article |
| ISSN: |
1778-3569 |
| DOI: |
10.5802/crmath.357 |
| Popis: |
In this paper, we analyse the long-time behavior of solutions to a coupled system describing the motion of a rigid disk in a 2D viscous incompressible fluid. Following previous approaches in [4, 15, 17] we look at the problem in the system of coordinates associated with the center of mass of the disk. Doing so, we introduce a further nonlinearity to the classical Navier Stokes equations. In comparison with the classical nonlinearities, this new term lacks time and space integrability, thus complicating strongly the analysis of the long-time behavior of solutions.We provide herein two refined tools: a refined analysis of the Gagliardo–Nirenberg inequalities and a thorough description of fractional powers of the so-called fluid-structure operator [2]. On the basis of these two tools we extend decay estimates obtained in [4] to arbitrary initial data and show local stability of the Lamb-Oseen vortex in the spirit of [7, 8]. |
| Databáze: |
Directory of Open Access Journals |
| Externí odkaz: |
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