We consider the cubic defocusing nonlinear Schrödinger equation in the two dimensional torus. Fix . Recently Colliander, Keel, Staffilani, Tao and Takaoka proved the existence of solutions with -Sobolev norm growing in time.
We establish the existence of solutions with polynomial time estimates. More exactly, there is such that for any we find a solution and a time such that . Moreover, the time satisfies the polynomial bound .
Cite this article
Marcel Guardia, Vadim Kaloshin, Growth of Sobolev norms in the cubic defocusing nonlinear Schrödinger equation. J. Eur. Math. Soc. 17 (2015), no. 1, pp. 71–149DOI 10.4171/JEMS/499