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].
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Guillaume Ferriere 1 ; Matthieu Hillairet 2
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@article{CRMATH_2023__361_G2_453_0,
author = {Guillaume Ferriere and Matthieu Hillairet},
title = {Unbounded-energy solutions to the fluid+disk system and long-time behavior for large initial data},
journal = {Comptes Rendus. Math\'ematique},
pages = {453--485},
publisher = {Acad\'emie des sciences, Paris},
volume = {361},
year = {2023},
doi = {10.5802/crmath.357},
language = {en},
}
TY - JOUR AU - Guillaume Ferriere AU - Matthieu Hillairet TI - Unbounded-energy solutions to the fluid+disk system and long-time behavior for large initial data JO - Comptes Rendus. Mathématique PY - 2023 SP - 453 EP - 485 VL - 361 PB - Académie des sciences, Paris DO - 10.5802/crmath.357 LA - en ID - CRMATH_2023__361_G2_453_0 ER -
%0 Journal Article %A Guillaume Ferriere %A Matthieu Hillairet %T Unbounded-energy solutions to the fluid+disk system and long-time behavior for large initial data %J Comptes Rendus. Mathématique %D 2023 %P 453-485 %V 361 %I Académie des sciences, Paris %R 10.5802/crmath.357 %G en %F CRMATH_2023__361_G2_453_0
Guillaume Ferriere; Matthieu Hillairet. Unbounded-energy solutions to the fluid+disk system and long-time behavior for large initial data. Comptes Rendus. Mathématique, Volume 361 (2023), pp. 453-485. doi : 10.5802/crmath.357. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.357/
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