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arXiv · 1202.1638

Non-Lipshitz flow of the nonlinear Schr\"odinger equation on surfaces

W. -M. Wang
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Abstract

We construct non-Lipshitz flow in $H^s$ for the cubic nonlinear Schr\"odinger equation on the 2-torus of revolution with a Lipshitz or smooth metric . The non-Lipshitz property holds for all $s<2/3$ for Lipshitz metric and $s<1/2$ for smooth metric. Both coincide with the Sobolev exponents for uniform local well-posedness.

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W. -M. Wang. 2012-02-08. Non-Lipshitz flow of the nonlinear Schr\"odinger equation on surfaces. https://arxiv.org/abs/1202.1638

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