广州数学大讲坛第十五期

第一百四十九讲——武汉大学江宁教授学术报告

题目:Grad-Caflisch type decay estimates of pseudo-inverse of linearized Boltzmann operator and application to Hilbert expansion of compressible Euler scaling

时间:20221125号(周五)上午9:00 -10:00

地点: 腾讯会议(会议号ID808-716-020

报告人:江宁  教授

 

摘要we prove some Grad-Caflisch type decay estimates of the pseudo-inverse of linearized Boltzmann collision operator, including both the hard potential(                                               ) and part of soft ( ) potential cutoff interaction kernels. The key idea is that the weighted -norms of  are first dominated by the weighted -norms of , and then the -norms are bounded by the -norms of  via the hypocoercivity of the weighted operator . The proof of the weighted hypocoercivity employs the high-low velocities estimates argument. Finally, these decay estimates are further applied to derive some new point-wise  estimates for the Hilbert expansion terms of the Boltzmann equation in the compressible Euler scaling.

报告人简介:

江宁,武汉大学数学与统计学院教授,博士生导师。本科毕业于南京大学数学系,硕士毕业于中科院数学所(导师为丁伟岳院士),博士毕业于美国马里兰大学(导师为C. D. Levermore教授)。2006-2010年在纽约大学Courant研究所任Courant讲师,2010-2015年在清华大学数学科学中心任教,2015年至今任武汉大学数学与统计学院教授。 江宁教授的研究方向为非线性偏微分方程和几何分析, 相关成果发表在CPAM, ARMA等国际著名期刊杂志上。