4/9/2012

Marcel Guardia
Universitat Politecnica de Catalunya / IAS

Growth of Sobolev norms for the cubic defocusing nonlinear Schrodinger equation in polynomial time

We consider the cubic defocusing nonlinear Schrodinger 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.