Diffusive limit for a Boltzmann-like equation with non-conserved momentum

Abstract

We consider a kinetic model whose evolution is described by a Boltzmann-like equation for the one-particle phase space distribution $f(x,v,t)$. There are hard-sphere collisions between the particles as well as collisions with randomly fixed scatterers. As a result, this evolution does not conserve momentum but only mass and energy. We prove that the diffusively rescaled $f^{\epsilon }(x,v,t)=f({\epsilon }^{-1}x,v,{\epsilon }^{-2}t)$, as $\epsilon \to 0$ tends to a Maxwellian $M_{\rho ,0,T}=\frac{\rho }{(2\pi T{)}^{3/2}}\exp [-\frac{|v{|}^2}{2T}]$, where $\rho$ and $T$ are solutions of coupled diffusion equations and estimate the error in $L_{x,v}^2$.

References in corpus (3)

• Stationary solutions to the Boltzmann equation in the Hydrodynamic limit
• Hydrodynamic Limit of a Kinetic Gas Flow Past an Obstacle
• Diffusion equations from kinetic models with non-conserved momentum

Cited by in corpus (1)

• Heat Conduction in a hard disc system with non-conserved momentum