## Young Researchers Workshop: Stochastic and deterministic methods in kinetic theory

### Log-log blow up solutions of NLS at exactly m points

Chenjie Fan

Massachusetts Institute of Technology
[SLIDES]

Abstract:

We will first introduce the log-log blow up solutions to NLS which have been studied by Merle and Raphael and many other authors. Then, we will illustrate our construction about certain solutions to NLS, which blow up at $m$ prescribed points according to log-log law. The idea is to use bootstrap to show the $m$ bubbles can be decoupled, and then use soft topological argument to balance different bubbles, making them blow up simultaneously at the prescribed points.