Global regularity and decay estimates for the relativistic Landau equation

Abstract: We consider the relativistic Landau equation in the spatially inhomogeneous, far-from-equilibrium regime. We establish regularity estimates of all orders, implying that solutions remain smooth for as long as some zeroth-order conditional bounds hold. We also prove that polynomial and exponential decay in the momentum variable is propagated forward in time. As part of our proof, we establish a Schauder estimate for linear relativistic kinetic equations, that may be of independent interest.