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.
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