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·▽ x f+f=M[f], t⩽0,x∈ R N ,v∈ R N M[f]=( p (2φT) N 2 ) exp ( −|v−u| 2 2T ), (p,pu,p|u| 2 +pT)(1,x)=∞ R N (1,v,|v| 2 )f(t,x,v)dv. It relies on the strong compactness of ϱ, u , T and on a new estimate on the third moment of ƒ: ∝ ¦v¦ ƒ dv . We also prove the entropy relation for (1).