Propagation of Gevrey regularity for solutions of Landau equations

TL;DR

This paper demonstrates how Gevrey regularity propagates over time for solutions to the spatially homogeneous Landau equation, specifically for Maxwellian molecules and hard potentials, using energy inequalities.

Contribution

It establishes the propagation of Gevrey regularity for Landau equation solutions, a novel result in the context of these specific molecular interactions.

Findings

Gevrey regularity propagates over time for Maxwellian molecules.

Gevrey regularity propagates over time for hard potential cases.

Energy inequalities are effective tools for proving regularity propagation.

Abstract

By using the energy-type inequality, we obtain, in this paper, the result on propagation of Gevrey regularity for the solution of the spatially homogeneous Landau equation in the cases of Maxwellian molecules and hard potential.