Blow-up Dynamics for $L^2$-critical Fractional Schr\"odinger Equations
发布时间：2018年07月03日
浏览次数：6653
发布者: He Liu
主讲人： Dr. Yang LAN (Basel University)
活动时间： 从 2018-07-16 14:00 到 16:00
场地： 北京国际数学研究中心，镜春园78号院（怀新园）78301室
We consider the $L^2$-critical fractional Schr\"odinger equation $iu_t-|D|^{\beta}u+|u|^{\frac{2\beta}{d}}u=0$ with initial data $u_0\in H^1(\mathbb{R}^d)$ and $\beta$ close to $2$. We will show that the solution blows up in finite time if the initial data has negative energy and slightly supercritical-mass. We will also give a specific description for the blow-up dynamics.
