The Boltzmann Equation Near Equilibrium

In this paper, we review some recent results on the Boltzmann equation near the equilibrium states in the whole space Rn. 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.