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

TL;DR

This paper establishes the local-in-time well-posedness of the relativistic Vlasov-Maxwell-Landau system with specular reflection boundary conditions in bounded domains, including non-convex shapes like solid tori, marking a first for such nonlinear kinetic models with magnetic effects.

Contribution

It provides the first local well-posedness proof for a nonlinear kinetic model with magnetic effects in a three-dimensional bounded domain.

Findings

Proves local-in-time well-posedness in non-convex domains.

Handles the relativistic Vlasov-Maxwell-Landau system with magnetic effects.

Includes domains with complex geometries like solid tori.

Abstract

We prove the local-in-time well-posedness of the relativistic Vlasov-Maxwell-Landau system in a bounded domain $\Omega$ with the specular reflection condition. Our result covers the case when $\Omega$ 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.