%0 Journal Article
%T Bounds on Sobolev norms for the nonlinear Schr£żdinger equation on general tori
%A F. Catoire
%A W. -M. Wang
%J Mathematics
%D 2008
%I arXiv
%X We prove Strichartz estimates on general flat d-torus for arbitrary d. Using these estimates, we prove local wellposedness for the cubic nonlinear Schr\"odinger equations in appropriate Sobolev spaces. In dimensions 2 and 3, we prove polynomial bounds on the possible growth of Sobolev norms of smooth solutions.
%U http://arxiv.org/abs/0809.4633v1