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Discrete velocity Boltzmann equations in the plane: stationary solutions

Leif Arkeryd and Anne Nouri

Vol. 16 (2023), No. 8, 1869–1884
Abstract

We prove the existence of stationary mild solutions for normal discrete velocity Boltzmann equations in the plane with no pair of colinear interacting velocities and given ingoing boundary values. We remove an important restriction from a previous paper that all velocities point into the same half-space. A key property is L1 compactness of integrated collision frequency for a sequence of approximations. This is proven using the Kolmogorov–Riesz theorem, which here replaces the L1 compactness of velocity averages in the continuous velocity case, not available when the velocities are discrete.

Keywords
stationary Boltzmann equation, discrete coplanar velocities, normal model
Mathematical Subject Classification
Primary: 60K35, 82C40, 82C99
Milestones
Received: 28 May 2021
Revised: 29 November 2021
Accepted: 14 February 2022
Published: 16 October 2023
Authors
Leif Arkeryd
Mathematical Sciences
Göteborg
Sweden
Anne Nouri
Aix-Marseille University
CNRS, I2M UMR 7373
Marseille
France

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