Analytic smoothing effect of linear landau equation with soft potential

TL;DR

This paper demonstrates that solutions to the linear Landau equation with soft potential become analytic over time, with their regularity evolving similarly to heat equations, starting from initial data in L2 space.

Contribution

It establishes the analytic smoothing effect for the linear Landau equation with soft potential, revealing the evolution of the analytic radius akin to heat equations.

Findings

Solutions gain analyticity over time.

Analytic radius evolves similarly to heat equations.

Initial data in L2 leads to analytic regularity.

Abstract

In this work, we study the linear Landau equation with soft potential and show that the solution to the Cauchy problem with initial datum in $L^{2}(\mathbb{R}^3)$ enjoys an analytic regularizing effect, and the evolution of analytic radius is same as heat equations.