Duan, Renjun The Boltzmann equation near equilibrium states in \(\mathbb R^N\). (English) Zbl 1157.76042 Methods Appl. Anal. 14, No. 3, 227-249 (2007). 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. Cited in 4 Documents MSC: 76P05 Rarefied gas flows, Boltzmann equation in fluid mechanics 76-02 Research exposition (monographs, survey articles) pertaining to fluid mechanics Keywords:well-posedness; asymptotical stability; energy estimates; spectral analysis PDFBibTeX XMLCite \textit{R. Duan}, Methods Appl. Anal. 14, No. 3, 227--249 (2007; Zbl 1157.76042) Full Text: DOI