The Boltzmann Equation Near Equilibrium States in $\mathbb R^n$

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

Keywords

Boltzmann equation, equilibrium state, energy estimates

2010 Mathematics Subject Classification

76P05, 82C40, 82D05

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Published 1 January 2007