Velocity Averaging Lemmas and Their Application to Boltzmann Equation

• Main Authors: Ping-Han Chuang, 莊秉翰
• Other Authors: I-Kun Chen
• Format: Others
• Language: en_US
• Published: 2019
• Online Access: http://ndltd.ncl.edu.tw/handle/atwrq4

碩士 === 國立臺灣大學 === 數學研究所 === 107 === In 1988, Golse, Lions, Perthame and Sentis jointly proved that velocity averaging has regularizing effects. This phenomenon was later called “Velocity Averaging Lemmas.” The Velocity Averaging Lemmas have significant applications in the global existence theory of the Cauchy problem for Boltzmann equations by DiPerna and Lions and also have many meaningful extensions themselves. In this thesis, we first review classical Velocity Averaging Lemmas, and then we present our new regularity results for the stationary linearized Boltzmann equation by velocity averaging effects.