Methods and Applications of Analysis
Volume 14 (2007)
The Boltzmann Equation Near Equilibrium States in $\mathbb R^n$
Pages: 227 – 250
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.
Boltzmann equation; equilibrium state; energy estimates
2010 Mathematics Subject Classification
76P05, 82C40, 82D05