Analytic smoothing effect of the time variable for the spatially homogeneous Landau equation

Chao-Jiang Xu, Yan Xu

Published 2022-06-06Version 1

In this work, we study the Cauchy problem of the spatially homogeneous Landau equation with hard potentials in a close-to-quilibrium framework. We prove that the solution to the Cauchy problem enjoys the analytic regularizing effect of the time variable with an L2 initial datum for positive time. So that the smoothing effect of Cauchy problem for the spatially homogeneous Landau equation with hard potentials is exactly same as heat equation.