Linear Landau Damping for the Vlasov-Maxwell System in \(\mathbb{R}^3\)

Abstract

In this work, we consider the relativistic Vlasov-Maxwell system, linearized around a spatially homogeneous equilibrium, set in the whole space \(\mathbb{R}^3 \times \mathbb{R}^3\). The equilibrium is assumed to belong to a class of radial, smooth, rapidly decaying functions. Under appropriate conditions on the initial data, we prove algebraic decay (of dispersive nature) for the electromagnetic field. For the electric scalar potential, the leading behavior is driven by a dispersive wave packet with non-degenerate phase and compactly supported amplitude, while for the magnetic vector potential, it is driven by a wave packet whose phase behaves globally like the one of Klein-Gordon and the amplitude has unbounded support.