Thermalization of a rarefied gas with total energy conservation: existence, hypocoercivity, macroscopic limit
arXiv:2012.07503 · doi:10.3934/krm.2022015
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 one-dimensional torus. Spectral stability of the equilibrium is shown on the torus in arbitrary dimensions by hypocoercivity methods. The macroscopic limit towards a nonlinear cross-diffusion problem is carried out formally.
References in corpus (9)
- Quantitative perturbative study of convergence to equilibrium for collisional kinetic models in the torus
- Hypocoercivity and exponential time decay for the linear inhomogeneous relaxation Boltzmann equation
- Exponential rate of convergence to equilibrium for a model describing fiber lay-down processes
- Existence, Uniqueness and Positivity of solutions for BGK models for mixtures
- Large-time behavior of solutions to Vlasov-Poisson-Fokker-Planck equations: from evanescent collisions to diffusive limit
- Decay to equilibrium for energy-reaction-diffusion systems
- Hypocoercivity and Fast Reaction Limit for Linear Reaction Networks with Kinetic Transport
- Hypocoercivity and reaction-diffusion limit for a nonlinear generation-recombination model
- Existence analysis of a degenerate diffusion system for heat-conducting fluids