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Special modes and hypocoercivity for linear kinetic equations with several conservation laws and a confining potential

Carrapatoso, Kleber; Dolbeault, Jean; Hérau, Frédéric; Mischler, Stéphane; Mouhot, Clément; Schmeiser, Christian (2021), Special modes and hypocoercivity for linear kinetic equations with several conservation laws and a confining potential. https://basepub.dauphine.psl.eu/handle/123456789/22083

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Type
Document de travail / Working paper
External document link
https://hal.archives-ouvertes.fr/hal-03222748
Date
2021
Series title
Cahier de recherche du CEREMADE
Pages
41
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Author(s)
Carrapatoso, Kleber
Centre de Mathématiques Laurent Schwartz [CMLS]
Institut Montpelliérain Alexander Grothendieck [IMAG]
Dolbeault, Jean cc
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Hérau, Frédéric cc
Laboratoire de Mathématiques Jean Leray [LMJL]
Département de Mathématiques et Informatique - Université de Nantes
Mischler, Stéphane
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Mouhot, Clément
Department of Pure Mathematics and Mathematical Statistics [DPMMS]
Schmeiser, Christian
Fakultät für Mathematik [Wien]
Faculty of Mathematics [Vienna]
Abstract (EN)
We study linear inhomogeneous kinetic equations with an external confining potential and a collision operator with several local conservation laws (local density, momentum and energy). We exhibit all equilibria and entropy-maximizing special modes, and we prove asymptotic exponential convergence of solutions to them with quantitative rate. This is the first complete picture of hypocoercivity and quantitative H-theorem for inhomogeneous kinetic equations in this setting.
Subjects / Keywords
hypocoercivity; Boltzmann equation; Landau equation; confining potential; weighted Korn inequality; micro-macro method; commutator method; Poincaré inequality