Special macroscopic modes and hypocoercivity

2021/05/11 by Kléber Carrapatoso, Carrapatoso, Kleber, Jean Dolbeault +9 · 1 citation
Mathematics · #35Q83 #76P05 #82C40 #82C70 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Gas Dynamics and Kinetic Theory #Mathematical Biology Tumor Growth #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.2105.04855

openalex publication_date 2021/05/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 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.

Cited by

• Discrete H-theorem for a finite volume discretization of a nonlinear kinetic system: application to hypocoercivity

Related

• Hypocoercivity for linear kinetic equations conserving mass
• Hypocoercivity without confinement
• Hypocoercivity of Linear Degenerately Dissipative Kinetic Equations
• Hypocoercivity and exponential time decay for the linear inhomogeneous relaxation Boltzmann equation
• Hypocoercivity for kinetic linear equations in bounded domains with general Maxwell boundary condition