Unbounded-energy solutions to the fluid+disk system and long-time behavior for large initial data
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 dis...
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Académie des sciences
2023-02-01
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| Series: | Comptes Rendus. Mathématique |
| Online Access: | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.357/ |
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| author | Ferriere, Guillaume Hillairet, Matthieu |
| author_facet | Ferriere, Guillaume Hillairet, Matthieu |
| author_sort | Ferriere, Guillaume |
| collection | DOAJ |
| description | 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]. |
| format | Article |
| id | doaj-art-58f634d24bda486daca202a5a9dbe4c1 |
| institution | Kabale University |
| issn | 1778-3569 |
| language | English |
| publishDate | 2023-02-01 |
| publisher | Académie des sciences |
| record_format | Article |
| series | Comptes Rendus. Mathématique |
| spelling | doaj-art-58f634d24bda486daca202a5a9dbe4c12025-02-07T11:06:36ZengAcadémie des sciencesComptes Rendus. Mathématique1778-35692023-02-01361G245348510.5802/crmath.35710.5802/crmath.357Unbounded-energy solutions to the fluid+disk system and long-time behavior for large initial dataFerriere, Guillaume0Hillairet, Matthieu1Institut de Recherche Mathématique Avancée, UMR 7501 Université de Strasbourg et CNRS, FranceIMAG, Univ Montpellier, CNRS, Montpellier, FranceIn 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].https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.357/ |
| spellingShingle | Ferriere, Guillaume Hillairet, Matthieu Unbounded-energy solutions to the fluid+disk system and long-time behavior for large initial data Comptes Rendus. Mathématique |
| title | Unbounded-energy solutions to the fluid+disk system and long-time behavior for large initial data |
| title_full | Unbounded-energy solutions to the fluid+disk system and long-time behavior for large initial data |
| title_fullStr | Unbounded-energy solutions to the fluid+disk system and long-time behavior for large initial data |
| title_full_unstemmed | Unbounded-energy solutions to the fluid+disk system and long-time behavior for large initial data |
| title_short | Unbounded-energy solutions to the fluid+disk system and long-time behavior for large initial data |
| title_sort | unbounded energy solutions to the fluid disk system and long time behavior for large initial data |
| url | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.357/ |
| work_keys_str_mv | AT ferriereguillaume unboundedenergysolutionstothefluiddisksystemandlongtimebehaviorforlargeinitialdata AT hillairetmatthieu unboundedenergysolutionstothefluiddisksystemandlongtimebehaviorforlargeinitialdata |