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Hypocoercivity for kinetic linear equations in bounded domains with general Maxwell boundary condition

Bernou, Armand; Carrapatoso, Kleber; Mischler, Stéphane; Tristani, Isabelle (2021), Hypocoercivity for kinetic linear equations in bounded domains with general Maxwell boundary condition. https://basepub.dauphine.psl.eu/handle/123456789/22157

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Type
Document de travail / Working paper
External document link
https://hal.archives-ouvertes.fr/hal-03142785
Date
2021
Series title
Cahier de recherche du CEREMADE
Published in
Paris
Pages
46
Metadata
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Author(s)
Bernou, Armand
Laboratoire Jacques-Louis Lions [LJLL (UMR_7598)]
Carrapatoso, Kleber
Centre de Mathématiques Laurent Schwartz [CMLS]
Mischler, Stéphane
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Tristani, Isabelle
Département de Mathématiques et Applications - ENS Paris [DMA]
Abstract (EN)
We establish the convergence to the equilibrium for various linear collisional kinetic equations (including linearized Boltzmann and Landau equations) with physical local conservation laws in bounded domains with general Maxwell boundary condition. Our proof consists in establishing an hypocoercivity result for the associated operator, in other words, we exhibit a convenient Hilbert norm for which the associated operator is coercive in the orthogonal of the global conservation laws. Our approach allows us to treat general domains with all type of boundary conditions in a unified framework. In particular, our result includes the case of vanishing accommodation coefficient and thus the specific case of the specular reflection boundary condition.