De nouveaux systèmes de type Kazhikhov–Smagulov : modèles de propagation de polluants et de combustion à faible nombre de Mach

Abstract

We propose some new Kazhikhov–Smagulov type models using particular Reynolds tensors depending on the relation between the velocity and the density. The pollutant spread model, for instance, has the advantage of possessing global weak solutions with no restriction on the data. Moreover, the model is obtained without assuming small enough diffusivity λ. In a general framework, several Kazhikhov–Smagulov type models may be derived and global existence of weak solutions established. This is the case for the low Mach number combustion model proposed by A. Majda. To cite this article: D. Bresch et al., C. R. Acad. Sci. Paris, Ser. I 335 (2002) 973–978.