Workshop - Problèmes mathématiques et modélisation en théorie cinétique

Marc Briant

The Boltzmann equation near global equilibrium in bounded domains

Although the study of the Boltzmann equation in a perturbative regime around a global equilibrium has been intensively studied in the whole space or the torus, very few is known when the spatial domain is bounded and non-periodic. We present some of the latest results in this field (Cauchy theory, trend to equilibrium, continuity of solutions...) when boundary conditions are either specular reflections or Maxwellian diffusion. The main purpose of this talk is to introduce the techniques (old and new) developed to obtain satisfying results - for instance, the cornerstone $L^2-L^\infty$ theory - as well as their drawbacks.

Partenaires

Irmar LMJL ENS Rennes LMBA LAREMA

Tutelles

ANR CNRS Rennes 1 Rennes 2 Nantes INSA Rennes INRIA ENSRennes UBO UBS Angers UBL