Blow-up Dynamics for $L^2$-critical Fractional Schr\"odinger Equations
Time: 2018-07-03
Published By: He Liu
Speaker(s): Dr. Yang LAN (Basel University)
Time: 14:00-16:00 July 16, 2018
Venue: Room 78301, Jingchunyuan 78, BICMR
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.
