## Global existence to the BGK model of Boltzmann equation.(English)Zbl 0694.35134

The author has proved results on existence and stability for solutions to the BGK model of Boltzmann equation (1) $\partial_ tf+v\cdot \nabla_ xf+f=M[f],\quad t\geq 0,\quad x\in {\mathbb{R}}^ N,\quad v\in {\mathbb{R}}^ N,$
$M[f]=(\rho /(2\pi T)^{N/2})\exp (-| v-u|^ 2/(2T)),$
$(\rho,\rho u,\rho | u|^ 2+\rho T)(t,x)=\int_{{\mathbb{R}}^ N}(1,v,| v|^ 2)f(t,x,v)dv.$ The proof mainly relies on the strong compactness of $$\rho$$, u, T and on a new estimate on the third moment of f: $$\int | v|^ 3f dv$$. The entropy relation for (1) is also proved.
Reviewer: B.G.Pachpatte

### MSC:

 35Q99 Partial differential equations of mathematical physics and other areas of application 76P05 Rarefied gas flows, Boltzmann equation in fluid mechanics 35B35 Stability in context of PDEs

### Keywords:

estimate; third moment; entropy relation
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### References:

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