Discrete velocity Boltzmann equations in the plane: stationary solutions

Leif Arkeryd , Anne Nouri (1)

1 AMU - Aix Marseille Université

The paper proves 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. An important restriction of all velocities pointing into the same half-space in a previous paper is removed in this paper. A key property is L 1 compactness of integrated collision frequency for a sequence of approximations. This is proven using the Kolmogorov-Riesz theorem, which here 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. Discrete velocity Boltzmann equations in the plane: stationary solutions. Documenta Mathematica, In press. ⟨hal-03523783⟩