Hypocoercivity for kinetic linear equations in bounded domains with general Maxwell boundary condition
Armand Bernou
Sorbonne University, Paris, FranceKleber Carrapatoso
Institut Polytechnique de Paris, Palaiseau, FranceStéphane Mischler
Université de Paris-Dauphine, Paris, FranceIsabelle Tristani
École Normale Supérieure - PSL, Paris, France
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Abstract
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 types 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.
Cite this article
Armand Bernou, Kleber Carrapatoso, Stéphane Mischler, Isabelle Tristani, Hypocoercivity for kinetic linear equations in bounded domains with general Maxwell boundary condition. Ann. Inst. H. Poincaré Anal. Non Linéaire 40 (2023), no. 2, pp. 287–338
DOI 10.4171/AIHPC/44