中科院数学与系统科学研究院

数学研究所

调和分析及其应用中心

学术报告会

报告人：Prof. Xu Chao jiang （University of Rouen, France）

题  目：Cauchy problem for the spatially homogeneous Landau equation with Shubin class initial datum

时  间：2017.09.26（星期二），10:30-11:30

地  点：数学院南楼N913室

摘  要：In this work, we study the nonlinear spatially homogeneous Landau equation with Maxwellian molecules, by using the spectral analysis, we show that the non linear Landau operators is almost linear, and we prove the existence of weak solution for the Cauchy problem with the initial datum belongs to Shubin space of negative index.  Based on this spectral decomposition, we also prove that the Cauchy problem enjoys Gelfand-Shilov smoothing effect, meaning that the weak solution of the Cauchy problem with Shubin class initial datum is ultra-analytics and exponential decay for any positive time.