On stationary kinetic systems of Boltzmann type and their fluid limits
Volume 66 / 2004
Abstract
The first part reviews some recent ideas and $L^1$-existence results for non-linear stationary equations of Boltzmann type in a bounded domain in ${\mathbb R}^{n}$ and far from global Maxwellian equilibrium. That is an area not covered by the DiPerna and P. L. Lions methods for the time-dependent Boltzmann equation from the late 1980-ies. The final part discusses the more classical perturbative case close to global equilibrium and corresponding small mean free path limits of fully non-linear stationary problems. Here the focus is on a particular two-rolls model problem including leading order hydrodynamic limits, but in a perspective of more general situations and the resolution of a variety of asymptotic stationary questions. Remarks are made about stationary solutions as long-time limits of corresponding time-dependent ones, and a number of open problems are also reviewed.
