Analytic Smoothing Effect of the Time Variable for the Spatially Homogeneous Landau Equation

Abstract

In this work, we study the Cauchy problem of the spatially homogeneous Landau equation with hard potentials in a close-to-equilibrium framework. We prove that the solution to the Cauchy problem enjoys the analytic regularizing effect of the time variable with an $L^2$ initial datum for positive time. So that the smoothing effect of the Cauchy problem for the spatially homogeneous Landau equation with hard potentials is exactly same as heat equation.