偏微分方程研讨班：Nonlinear Heat and Nonlocal Schrödinger Equations in Super-Critical Spaces

中科院数学与系统科学研究院

数学研究所

偏微分方程研讨班

报告人： 王保祥 教授（北京大学）

题  目：Nonlinear Heat and Nonlocal Schrödinger Equations in Super-Critical Spaces

时  间：2021.12.08（星期三），10:30-11:30

地  点：腾讯会议：786 604 336

摘  要：We consider the Cauchy problem for the semi-linear heat, nonlocal Schr\"odinger equations in super-critical spaces $E^s$ for which the norms are defined by

        $$\|f\|_{E^s} = \|2^{s|\xi|}\widehat{f}(\xi)\|_{L^2}, \ s<0.$$

If $s<0$, then any Sobolev space $H^{r}$ is a subspace of $E^s$, i.e., $\cup_{r \in \mathbb{R}} H^r \subset E^s$. We will obtain the global existence and uniqueness of the solutions if the initial data belong to $E^s$ and their Fourier transforms are supported in the first octant and away from the origin, the smallness conditions on the initial data in $E^s$ are not required for the global solutions.This is a joint work with Dr. Jie Chen.