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      Discrete velocity Boltzmann equation in the plane: stationary solutions

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          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.

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          Author and article information

          Journal
          16 December 2021
          Article
          2112.08640
          3175aba7-ad90-4906-a449-b4e87e9a0756

          http://creativecommons.org/licenses/by/4.0/

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          Custom metadata
          60K35, 82C40, 82C99
          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
          math.AP math-ph math.MP

          Mathematical physics,Analysis,Mathematical & Computational physics
          Mathematical physics, Analysis, Mathematical & Computational physics

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