The Local-well-posedness of the relativistic Vlasov-Maxwell-Landau system with the specular reflection boundary condition

Abstract

We prove the local-in-time well-posedness of the relativistic Vlasov-Maxwell-Landau system in a bounded domain $Ω$ with the specular reflection condition. Our result covers the case when $Ω$ is a non-convex domain, e.g., solid torus. To the best of our knowledge, this is the first local well-posedness result for a nonlinear kinetic model with a self-consistent magnetic effect in a three-dimensional $\textbf{bounded}$ domain.