Analytic Gelfand-Shilov smoothing effect of the spatially homogeneous Landau equation with hard potentials

Abstract

In this work, we give an improved new argument to prove that the solution of the Cauchy problem for the nonlinear spatially homogeneous Landau equation with hard potentials with $ L^2(\mathbb{R}^3) $ initial datum enjoys a analytic Gelfand-Shilov regularizing effect in the class $ S^1_1(\mathbb{R}^3) $, the evolution of analytic radius is similar to the heat equation.