Methods and Applications of Analysis

Volume 14 (2007)

Number 3

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

Pages: 227 – 250

DOI: http://dx.doi.org/10.4310/MAA.2007.v14.n3.a2

Author

Renjun Duan

Abstract

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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