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

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

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Marcel Guardia, Universitat Politecnica de Catalunya & IAS
Fine Hall 314

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.