Stationary solutions to the Boltzmann equation in the plane

Abstract

The paper proves existence of stationary solutions to the Boltzmann equation in a bounded set of R 2 \mathbb {R}^2 for given indata, hard forces and truncation in the collision kernel for small velocities and close to parallel colliding velocities. It does not use any averaging in velocity lemma. Instead, it is based on stability techniques employing the Kolmogorov-Riesz-Fréchet theorem, from the discrete velocity stationary case, where the averaging in velocity lemmas are not valid.