Regularity of the spatially homogenous fractional Kramers-Fokker-Planck equation

TL;DR

This paper investigates the regularity and decay properties of solutions to the spatially homogenous fractional Kramers-Fokker-Planck equation, demonstrating Gevrey regularity and decay estimates for positive times starting from L2 initial data.

Contribution

It establishes Gevrey regularity and decay estimates for solutions of the fractional Kramers-Fokker-Planck equation with L2 initial data, advancing understanding of its regularity properties.

Findings

Solutions exhibit Gevrey regularity for positive times.

Decay estimates are established for solutions.

Regularity results hold starting from L2 initial data.

Abstract

We study the Cauchy problem of the spatially homogenous fractional Kramers-Fokker-Planck equation and show that the solution enjoys Gevrey regularity and decay estimation with an L2 initial datum for positive time.