Analytic smoothing effect of Cauchy problem for a class of Kolmogorov-Fokker-Planck equations

TL;DR

This paper demonstrates that solutions to a class of Kolmogorov-Fokker-Planck equations become analytic over time, even with only L2 initial data, highlighting a smoothing effect in the solutions.

Contribution

It establishes the analytic smoothing effect for solutions of Kolmogorov-Fokker-Planck equations starting from L2 initial data, which was previously not well understood.

Findings

Solutions become analytic for positive time

Smoothing effect holds for L2 initial data

Provides new insights into regularity of Kolmogorov-Fokker-Planck equations

Abstract

We study the Cauchy problem of the Kolmogorov-Fokker-Planck equations and show that the solution enjoys an analytic smoothing effect with L2 initial datum for positive time.