Thermalization of a rarefied gas with total energy conservation: existence, hypocoercivity, macroscopic limit
Abstract
The thermalization of a gas towards a Maxwellian velocity distribution with the background temperature is described by a kinetic relaxation model. The sum of the kinetic energy of the gas and the thermal energy of the background are conserved, and the heat flow in the background is governed by the Fourier law. For the coupled nonlinear system of the kinetic and the heat equation, existence of solutions is proved on the onedimensional torus. Spectral stability of the equilibrium is shown on the torus in arbitrary dimensions by hypocoercivity methods. The macroscopic limit towards a nonlinear crossdiffusion problem is carried out formally.
 Publication:

arXiv eprints
 Pub Date:
 December 2020
 DOI:
 10.48550/arXiv.2012.07503
 arXiv:
 arXiv:2012.07503
 Bibcode:
 2020arXiv201207503F
 Keywords:

 Mathematics  Analysis of PDEs
 EPrint:
 doi:10.3934/krm.2022015