Communications in Mathematical Sciences

Volume 18 (2020)

Number 8

On stationary solutions to normal, coplanar discrete Boltzmann equation models

Pages: 2215 – 2234



Leif Arkeryd (Mathematical Sciences, University of Gothenburg and Chalmers, Goteborg, Sweden)

Anne Nouri (Institut de Mathématiques de Marseille, Aix-Marseille University, Marseille, France)


The paper proves existence of renormalized solutions for a class of velocity-discrete coplanar stationary Boltzmann equations with given indata. The proof is based on the construction of a sequence of approximations with $L^1$ compactness for the integrated collision frequency and gain term. $L^1$ compactness of a sequence of approximations is obtained using the Kolmogorov–Riesz theorem and replaces the $L^1$ compactness of velocity averages in the continuous velocity case, not available when the velocities are discrete.


stationary Boltzmann equation, discrete coplanar velocities, normal model, entropy

2010 Mathematics Subject Classification

60K35, 82C40, 82C99

Received 12 March 2020

Accepted 9 June 2020

Published 22 December 2020