题目：From Morawetz inequality to the asymptotic distribution of energy of solutions to wave equations
会议 ID：441 183 021
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.