×

zbMATH — the first resource for mathematics

Solutions of the Boltzmann equation. (English) Zbl 0633.76078
Patterns and waves. Qualitative analysis of nonlinear differential equations, Stud. Math. Appl. 18, 37-96 (1986).
[For the entire collection see Zbl 0604.00007.]
This note is devoted to the review of the major results obtained in these ten years on the existence problem for the Boltzmann equation. The topics cover the local and global existence theorems for a variety of the Cauchy and initial boundary value problems, the existence and stability of the stationary solution for an exterior problem and the relation between the Boltzmann equation and fluid dynamics. They will be presented with emphasis on mathematical ideas of proofs. Also, important open problems will be pointed out.

MSC:
76P05 Rarefied gas flows, Boltzmann equation in fluid mechanics
82B40 Kinetic theory of gases in equilibrium statistical mechanics
76-02 Research exposition (monographs, survey articles) pertaining to fluid mechanics