On stationary solutions to normal, coplanar discrete Boltzmann equation models

Leif Arkeryd (1) , Anne Nouri (2)

1 Chalmers University of Technology [Göteborg]
2 LATP - Laboratoire d'Analyse, Topologie, Probabilités

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. .

Domaines: Equations aux dérivées partielles [math.AP]

Leif Arkeryd, Anne Nouri. On stationary solutions to normal, coplanar discrete Boltzmann equation models. 2020. ⟨hal-02520761⟩