Solutions globales de l’équation de Boltzmann. (Global solutions of the Boltzmann equation). (French) Zbl 0662.35016

Di Perna, Ronald; Lions, Pierre-Louis

C. R. Acad. Sci., Paris, Sér. I 306, No. 7, 343-346 (1988).

We prove the stability and existence of global solutions of Boltzmann equations under general assumptions on the collision operators and the initial conditions. In particular, we introduce a new formulation of the equation and we observe some weak continuity properties of the collision operator.

MSC:

35G25	Initial value problems for nonlinear higher-order PDEs
35Q99	Partial differential equations of mathematical physics and other areas of application
76P05	Rarefied gas flows, Boltzmann equation in fluid mechanics
35A05	General existence and uniqueness theorems (PDE) (MSC2000)
35B35	Stability in context of PDEs
82C70	Transport processes in time-dependent statistical mechanics

Keywords:

stability; existence; global solutions; Boltzmann equations; collision operators; initial conditions; weak continuity