Microlocal analysis on PDE : Some contributions by Yoshinori Morimoto around kinetic equations (Workshop on the Boltzmann Equation, Microlocal Analysis and Related Topics)

Abstract

In this short paper, we give a brief presentation of some contribution to microlocal analysis on the partial differential equations by Yoshinori Morimoto. The first part concerns the study of the degenerate elliptic equations, by using the microlocal analysis based on the theory of pseudo-differential operators. The second part is about the analysis of non-cutoff Boltzmann equations where the microlocal analysis contribute lots of progress, in particular, using Fefferman-Phong's uncertainty principle to prove the smoothing effect of solutions and Littlewood-Paley theory to study the existence of classical solutions for non-cutoff Boltzmann equations. So that we focus only on the contribution to the study of kinetic equations by Yoshinori Morimoto.