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arXiv · 0809.4633

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

F. Catoire·W. -M. Wang
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Abstract

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.

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F. Catoire, W. -M. Wang. 2008-09-26. Bounds on Sobolev norms for the nonlinear Schrödinger equation on general tori. https://arxiv.org/abs/0809.4633

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