English

Special macroscopic modes and hypocoercivity

Analysis of PDEs 2024-07-11 v5 Mathematical Physics math.MP

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.

Keywords

Cite

@article{arxiv.2105.04855,
  title  = {Special macroscopic modes and hypocoercivity},
  author = {Kleber Carrapatoso and Jean Dolbeault and Frédéric Hérau and Stéphane Mischler and Clément Mouhot and Christian Schmeiser},
  journal= {arXiv preprint arXiv:2105.04855},
  year   = {2024}
}

Comments

65 pages, 1 figure

R2 v1 2026-06-24T01:58:37.976Z