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March  2010, 9(2): 483-491. doi: 10.3934/cpaa.2010.9.483

## Bounds on Sobolev norms for the defocusing nonlinear Schrödinger equation on general flat tori

 1 Département de Mathématique, Université Paris Sud, 91405 Orsay Cedex, France, France

Received  March 2009 Revised  August 2009 Published  December 2009

We prove Strichartz estimates on general flat $d$-torus for arbitrary $d$. Using these estimates, we prove local wellposedness for the cubic nonlinear Schrödinger equations in appropriate Sobolev spaces. In dimensions $2$ and $3$, we prove polynomial bounds on the possible growth of Sobolev norms of smooth solutions.
Citation: F. Catoire, W. M. Wang. Bounds on Sobolev norms for the defocusing nonlinear Schrödinger equation on general flat tori. Communications on Pure & Applied Analysis, 2010, 9 (2) : 483-491. doi: 10.3934/cpaa.2010.9.483
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