Title: A remark on normal forms and the upside-down I-method for periodic NLS: growth of higher Sobolev norms

Speaker: Soonsik Kwon (Department of Mathematical Science, Korea Advanced Institute of Science and Technology）

Venue: Room 29 at Quan-Zhai (全斋), New location for BICMR, Peking University

Time: March 27, 2012, Tuesday, 3:30-4:30pm

Abstract: We study growth of higher Sobolev norms of solutions to the one-dimensional periodic nonlinear Schro ̈dinger equation (NLS). It is well-known that growth of Sobolev norm is at most polynomial rate by Bourgain, and other works. Here we use the normal form reduction and the upside-down I-method to reprove this and improve known result for some case. I will discuss the idea of normal form reduction and how we combine that with upside-down I-method. This is a collaboration with Jim Colliander and Tadahiro Oh.