English

Discrete velocity Boltzmann equation in the plane: stationary solutions

Analysis of PDEs 2023-10-25 v1 Mathematical Physics math.MP

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.

Keywords

Cite

@article{arxiv.2112.08640,
  title  = {Discrete velocity Boltzmann equation in the plane: stationary solutions},
  author = {Leif Arkeryd and Anne Nouri},
  journal= {arXiv preprint arXiv:2112.08640},
  year   = {2023}
}

Comments

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