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

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.