Convergence of weak solutions for the stationary Vlasov-Maxwell system to weak solutions for the stationary Vlasov-Poisson system for infinite light speed.
The author analyzes the behaviour of weak solutions for the relativistic stationary Vlasov-Maxwell system, when the underlying domain \(\Omega\) is an open bounded set in \(\mathbb{R}^3\). Assuming the boundary \(\partial\Omega\) is regular and strictly star-shaped, and using weak stability results, he proves the convergence toward a weak solution for the stationary classical Vlasov-Poisson system. One of the main difficulties consists in removing the dependence on the light speed in the vacuum of the bound for the outgoing kinetic energy. The author states that the time periodic and the initial-boundary value problems can be treated analogously.
scientific article; zbMATH DE number 2182043
scientific article