Regularity for the Boltzmann Equation Conditional to Pressure and Moment Bounds

Abstract

We prove that solutions to the Boltzmann equation without cut-off satisfying pointwise bounds on some observables (mass, pressure, and suitable moments) enjoy a uniform bound in L∞ in the case of hard potentials. As a consequence, we derive C∞ estimates and decay estimates for all derivatives, conditional to these macroscopic bounds. Our L∞ estimates are uniform in the limit s 1 and hence we recover the same results also for the Landau equation.