Special macroscopic modes and hypocoercivity

Kleber Carrapatoso; Jean Dolbeault; Frédéric Hérau; Stéphane Mischler; Clément Mouhot; Christian Schmeiser

doi:10.4171/jems/1502

Special macroscopic modes and hypocoercivity

Kleber Carrapatoso
, Jean Dolbeault
, Frédéric Hérau
, Stéphane Mischler
, Clément Mouhot
, Christian Schmeiser

Université Paris Dauphine
Laboratoire de Mathématiques Jean Leray
University of Cambridge
University of Vienna

Résultats de recherche: Contribution à un journal › Article › Revue par des pairs

Résumé

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 nontrivial 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.

langue originale	Anglais
Pages (de - à)	1597-1659
Nombre de pages	63
journal	Journal of the European Mathematical Society
Volume	28
Numéro de publication	4
Les DOIs	https://doi.org/10.4171/jems/1502
état	Publié - 18 févr. 2026

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10.4171/jems/1502

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title = "Special macroscopic modes and hypocoercivity",

abstract = "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 nontrivial 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.",

keywords = "Poincar{\'e}–Korn inequality, Witten–Laplace operator, classification of steady states, collision invariant, collision operator, confinement potential, conservation laws, hypocoercivity, hypoellipticity, linear kinetic equations, local conservation laws, micro/macro decomposition, partially harmonic potential, special macroscopic modes, spectral gap, time-periodic solutions, transport operator",

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T1 - Special macroscopic modes and hypocoercivity

AU - Carrapatoso, Kleber

AU - Dolbeault, Jean

AU - Hérau, Frédéric

AU - Mischler, Stéphane

AU - Mouhot, Clément

AU - Schmeiser, Christian

PY - 2026/2/18

Y1 - 2026/2/18

N2 - 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 nontrivial 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.

AB - 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 nontrivial 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.

KW - Poincaré–Korn inequality

KW - Witten–Laplace operator

KW - classification of steady states

KW - collision invariant

KW - collision operator

KW - confinement potential

KW - conservation laws

KW - hypocoercivity

KW - hypoellipticity

KW - linear kinetic equations

KW - local conservation laws

KW - micro/macro decomposition

KW - partially harmonic potential

KW - special macroscopic modes

KW - spectral gap

KW - time-periodic solutions

KW - transport operator

UR - https://www.scopus.com/pages/publications/105030960981

U2 - 10.4171/jems/1502

DO - 10.4171/jems/1502

M3 - Article

AN - SCOPUS:105030960981

SN - 1435-9855

VL - 28

SP - 1597

EP - 1659

JO - Journal of the European Mathematical Society

JF - Journal of the European Mathematical Society

IS - 4

ER -

Special macroscopic modes and hypocoercivity

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