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

• Xu, Chao-Jiang

  Université de Rouen, CNRS, UMR 6085-Laboratoire de Mathématiques・School of Mathematics and Statistics, Wuhan University

抄録

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.

"Workshop on the Boltzmann Equation, Microlocal Analysis and Related Topics". May 27～29, 2016. edited by Hisashi Okamoto, Yoshio Tsutsumi, Naomasa Ueki, Tadayoshi Adachi and Senjo Shimizu. The papers presented in this volume of RIMS Kôkyûroku Bessatsu are in final form and refereed.

収録刊行物

• 数理解析研究所講究録別冊

  数理解析研究所講究録別冊 B67 137-154, 2017-10

  Research Institute for Mathematical Sciences, Kyoto University

キーワード

• 35A05
• 35B65
• 35D10
• 35H20
• 76P05
• 84C40
• Microlocal analysis
• hypoellipticity
• uncertainty principle
• Littlewood-Paley theory
• non-cutoff Boltzmann equations

詳細情報

• CRID: 1050282813437269632
• NII論文ID: 120006715433
• NII書誌ID: AA12196120
• ISSN: 18816193
• HANDLE: 2433/243709
• 本文言語コード: en
• 資料種別: departmental bulletin paper
• データソース種別:
  • IRDB
  • CiNii Articles