Bounds on Sobolev norms for the nonlinear Schrödinger equation on general tori

Details Bounds on Sobolev norms for the nonlinear Schrödinger equation on general tori Bounds on Sobolev norms for the nonlinear Schrödinger equation on general tori

2008-09-26

arxiv.org/abs/0809.4633v1

Mathematics

Analysis of PDEs

Scientific paper

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.

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