Regularization properties of the 2-dimensional non radially symmetric non cutoff spatially homogeneous Boltzmann equation for Maxwellian molecules

Abstract

We prove in this work that the solution of the two-dimensional spatially homogeneous Boltzmann equation with Maxwellian molecules lies “almost” in H 1 (in the velocity variable) as soon as the initial datum has finite mass, energy and entropy. No assumption of radial symmetry of the solution is made in this paper.