Regularity of Non-cutoff Boltzmann Equation with Hard Potential

TL;DR

This paper establishes the regularity of solutions to the non-cutoff Boltzmann equation with hard potential, demonstrating smoothing effects in space and velocity variables under mild initial regularity conditions.

Contribution

It refines coercivity and upper bounds on the collision operator and analyzes Poisson brackets to prove regularity for the non-cutoff Boltzmann equation with hard potential.

Findings

Proves regularity in space and velocity variables.

Shows regularizing effect with mild initial data.

Sharpened estimates on collision operator.

Abstract

This article proves the regularity for the Boltzmann equation without angular cutoff with hard potential. By sharpening the coercivity and upper bound estimate on the collision operator, analyzing the Poisson bracket between the transport operator and some weighted pseudo-differential operator, we prove the regularizing effect in space and velocity variables when the initial data has mild regularity.