05-06【沈瑞鹏】腾讯会议 吴文俊数学重点实验室微分方程系列报告之7

发布者:万宏艳发布时间:2021-04-28浏览次数:156

题目:From Morawetz inequality to the asymptotic distribution of energy of solutions to wave equations


报告人:沈瑞鹏(天津大学)


时间:5月6日星期四 19:30-20:30


地点:腾讯会议 点击链接入会,或添加至会议列表:https://meeting.tencent.com/s/S0S0vwa5y8nH


会议 ID:441 183 021


会议密码:123456


摘要:Morawetz estimates of wave/Klein-Gordon equations were first found by Morawetz in a short paper in 1968. Nowadays Morawetz estimates have become one of the most important tools in the study of defocusing Schrodinger or wave equations. In this talk we consider the energy sub-critical wave equations and discuss how to deduce an Morawetz identity instead of an inequality, then obtain the asymptotic property of energy distribution. As an application we prove the scattering of solutions with a weaker assumption on the decay rate of initial data than previously known results. We first discuss higher dimensional case $d\geq 3$, then talk about the technical difficulties in dimension 2 and the techniques to overcome these difficulties.