Global existence to the BGK model of Boltzmann equation

Abstract

We present an existence and a stability proof for solutions to the BGK model of Boltzmann Equation δ,f+v·▽xf+f=M[f], t≤0,x∈RN,v∈RN M[f]=( p (2φT) N 2)exp( -|v-u|2 2T), (p,pu,p|u|2+pT)(1,x)=∞RN(1,v,|v| 2)f(t,x,v)dv. It relies on the strong compactness of ρ{variant}, u, T and on a new estimate on the third moment of f{hook}: ∝ |v| f{hook} dv. We also prove the entropy relation for (1). © 1989.