LITTLEWOOD–PALEY THEORY AND REGULARITY ISSUES IN BOLTZMANN HOMOGENEOUS EQUATIONS I: NON-CUTOFF CASE AND MAXWELLIAN MOLECULES

Abstract

We use Littlewood–Paley theory for the analysis of regularization properties of solutions of the homogeneous Boltzmann equation. For non-cutoff Maxwellian molecules, we show that such solutions are smoother than the initial data. Although the recent and up to date results of Desvillettes and Wennberg10 assume much more general assumptions on the collision cross sections, our method seems to be simpler than those used earlier to show such properties and also applies to any weak solution.