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Global derivation of a Boussinesq–Navier–Stokes type system from fluid-kinetic equations
Lucas Ertzbischoff1
1 Centre de Mathématiques Laurent Schwartz (UMR 7640), Ecole polytechnique, Institut Polytechnique de Paris, 91128 Palaiseau Cedex, France
Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 33 (2024) no. 4, pp. 1059-1154.

We study a hydrodynamic limit of the Vlasov–Navier–Stokes system with external gravity force. We answer a question raised by Han-Kwan and Michel in [48] concerning the limit towards a Boussinesq–Navier–Stokes type system. Our work provides a rigorous derivation of such hydrodynamic equations for arbitrarily large times, starting from the previous fluid-kinetic coupling. To do so, we consider a particular spatial geometric setting corresponding to the half-space case. Our proof is based on an absorption effect at the boundary which leads to crucial decay in time estimates.

Nous étudions une limite hydrodynamique du système de Vlasov–Navier–Stokes avec une force de gravité extérieure. Nous répondons ici à une question soulevée par Han-Kwan et Michel concernant la limite vers un système de type Boussinesq–Navier–Stokes. Notre travail établit une dérivation rigoureuse de ces équations hydrodynamiques pour des temps arbitrairement grands, à partir du couplage fluide-cinétique précédent. Pour ce faire, nous considérons un cadre géométrique spatial particulier correspondant au cas du demi-espace. Notre preuve est basée sur un effet crucial d’absorption au bord qui conduit à des estimations de décroissance en temps.

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DOI: 10.5802/afst.1796

Lucas Ertzbischoff 1

1 Centre de Mathématiques Laurent Schwartz (UMR 7640), Ecole polytechnique, Institut Polytechnique de Paris, 91128 Palaiseau Cedex, France
License: CC-BY 4.0
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     title = {Global derivation of a {Boussinesq{\textendash}Navier{\textendash}Stokes} type system from fluid-kinetic equations},
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Lucas Ertzbischoff. Global derivation of a Boussinesq–Navier–Stokes type system from fluid-kinetic equations. Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 33 (2024) no. 4, pp. 1059-1154. doi : 10.5802/afst.1796. https://afst.centre-mersenne.org/articles/10.5802/afst.1796/

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