Regularizing effect of the spatially homogeneous Landau equation with soft potential

TL;DR

This paper studies the spatially homogeneous Landau equation with soft potential, demonstrating that solutions become analytic over time and exhibit strong regularization in velocity variables.

Contribution

It proves the analyticity in time and Gelfand-Shilov regularization in velocity for solutions to the Landau equation with soft potential.

Findings

Solutions are analytic in time.

Solutions exhibit Gelfand-Shilov regularization in velocity.

Global existence near equilibrium is established.

Abstract

This paper investigates the Cauchy problem of the spatially homogeneous Landau equation with soft potential under the perturbation framework to global equilibrium. We prove that the solution to the Cauchy problem exhibits analyticity in the time variable and the Gelfand-Shilov regularizing effect in the velocity variables.