Analytic smoothness effect of solutions for spatially homogeneous Landau equation

TL;DR

This paper investigates how solutions to the spatially homogeneous Landau equation become smoother over time, demonstrating analytic smoothing effects under weak initial data assumptions for specific potential cases.

Contribution

It establishes the analytic smoothing effect for solutions of the Landau equation in the hard potential and Maxwellian molecules cases, with weak initial data assumptions.

Findings

Solutions exhibit analytic smoothing effects over time.

Weak initial data assumptions are sufficient for smoothing.

Results apply to specific potential cases.

Abstract

In this paper, we study the smoothness effect of Cauchy problem for the spatially homogeneous Landau equation in the hard potential case and the Maxwellian molecules case. We obtain the analytic smoothing effect for the solutions under rather weak assumptions on the initial datum.