Non-Lipshitz flow of the nonlinear Schr\"odinger equation on surfaces
Abstract
We construct non-Lipshitz flow in Hs 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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