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


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
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