Analysis Seminar

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Growth of Sobolev Norms for the Cubic Defocusing Nonlinear Schrödinger Equation in Polynomial Time

Speaker: Marcel Guardia, IAS

Location: Warren Weaver Hall 1302

Date: Thursday, April 19, 2012, 10 a.m.

Synopsis:

We consider the cubic defocusing nonlinear Schrödinger equation in the two dimensional torus. Fix s>1. Colliander, Keel, Staffilani, Tao and Takaoka (2010) proved existence of solutions with s-Sobolev norm growing in time by any given factor R. Refining their methods in several aspects we find solutions with s-Sobolev norm growing in polynomial time in R. This is a joint work with V. Kaloshin.