Discrete velocity Boltzmann equation in the plane: stationary solutions

Abstract

The paper proves existence of mild solutions to normal discrete velocity Boltzmann equations sin the plane with no pair of colinear interacting velocities, and given ingoing boundary values. A key property is L1 compactness of the integrated collision frequency for a sequence of approximations. This is proved using the Kolmogorov-Riesz theorem, which here replaces the L1 compactness of velocity averages, not available when the velocities are discrete.

The velocity conditions are more general than in the previous version. The end of proof, Section 4, is changed. The appendix is replaced with a reference to the paper where those background properties were first proved. arXiv admin note: substantial text overlap with arXiv:2101.11922, arXiv:2007.02094