Gevrey and Gelfand–Shilov smoothing effect for the spatially inhomogeneous Landau equation with hard potentials

Abstract

Abstract In this work, we study the Cauchy problem of the spatially inhomogeneous Landau equation with hard potential in torus. It is showed that the smooth mild solution near Maxwellians to the Cauchy problem enjoys a Gelfand–Shilov regularizing effect in velocity variable and Gevrey smoothness property in space variable.