Special macroscopic modes and hypocoercivity

Carrapatoso, Kleber; Dolbeault, Jean; Hérau, Frédéric; Mischler, Stéphane; MOUHOT, CLEMENT; Schmeiser, Christian

Carrapatoso, Kleber; Dolbeault, Jean; Hérau, Frédéric; Mischler, Stéphane; MOUHOT, CLEMENT; Schmeiser, Christian (2022), Special macroscopic modes and hypocoercivity. https://basepub.dauphine.psl.eu/handle/123456789/22083

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Type

Document de travail / Working paper

Date

2022

Series title

Cahier de recherche CEREMADE, Université Paris Dauphine-PSL

Published in

Paris

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Author(s)

Carrapatoso, Kleber
Dolbeault, Jean
Hérau, Frédéric
Mischler, Stéphane
MOUHOT, CLEMENT
Schmeiser, Christian

Abstract (EN)

We study linear inhomogeneous kinetic equations with an external confining potential and a collision operator admitting several local conservation laws (local density, momentum and energy). We classify all special macroscopic modes (stationary solutions and time-periodic solutions). We also prove the convergence of all solutions of the evolution equation to such non-trivial modes, with a quantitative exponential rate. This is the first hypocoercivity result with multiple special macroscopic modes with constructive estimates depending on the geometry of the potential.

Subjects / Keywords

hypocoercivity; linear kinetic equations; collision operator; transport operator; collision invariant; local conservation laws; micro/macro decomposition; commutators; hypoellipticity; confinement potential; rotations; rotational invariance; symmetries; global conservation laws; spectral gap; Poincaré-Korn inequality; Witten-Laplace operator; partially harmonic potential; time-periodic solutions; classification of steady states; special macroscopic modes