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The Boltzmann equation near equilibrium states in \(\mathbb R^N\). (English) Zbl 1157.76042

Summary: We review some recent results on the Boltzmann equation near equilibrium states in the whole space \(\mathbb R^n\). The emphasize is put on the well-posedness of the solution in some Sobolev spaces without time derivatives, on its uniform stability and optimal decay rates, and also on the existence and asymptotical stability of the time-periodic solution. Most of results are proved by combining energy estimates and spectral analysis.

MSC:

76P05 Rarefied gas flows, Boltzmann equation in fluid mechanics
76-02 Research exposition (monographs, survey articles) pertaining to fluid mechanics
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