The Boltzmann Equation Near Equilibrium States in $\mathbb R^n$
Renjun Duan · Methods and Applications of Analysis · 2007
In this paper, we review some recent results on the Boltzmann equation near the equilibrium states in the whole space 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.