Asymptotic Stability for Relativistic Vlasov-Maxwell-Landau System in Bounded Domain

Abstract

The control of plasma-wall interactions is crucial to fusion devices from both physical and mathematical perspectives. It is well known that a magnetic field satisfying the classical perfect conducting conditions at the wall, $$ \mathbf{E} \times n_x = 0, \quad \mathbf{B} \cdot n_x = 0, $$ plays an important role in fusion plasma dynamics studies. Since the early 1990s, it has been understood that the Lorentz force can penetrate into the domain at the boundary and create a singularity. Consequently, the uniqueness for any nonlinear kinetic plasma models in the presence of a perfectly conducting boundary remained open until our recent local well-posedness result. In this paper, we finally establish a global well-posedness theory for the relativistic Vlasov-Maxwell-Landau system in a general $3D$ domain with a specularly reflective, perfectly conducting boundary.