On exponential moments of the homogeneous Boltzmann equation for hard potentials without cutoff

TL;DR

This paper proves that exponential moments are immediately generated and propagated in the homogeneous Boltzmann equation for hard potentials without cutoff, showing stronger results than with cutoff.

Contribution

It establishes the creation and propagation of exponential moments for the Boltzmann equation without cutoff, extending previous results to a more general setting.

Findings

Exponential moments of order $ ho$ are immediately created.

Exponential moments of order $ ho ext{ in } (0,2]$ are propagated.

Stronger exponential moment results than in the cutoff case.

Abstract

We consider the spatially homogeneous Boltzmann equation for hard potentials without cutoff. We prove that an exponential moment of order $\rho=\min\{2\gamma/(2-\nu),2\}$, with the usual notation, is immediately created. This is stronger than what happens in the case with cutoff. We also show that exponential moments of order $\rho\in (0,2]$ are propagated.