Non-Lipshitz flow of the nonlinear Schrödinger equation on surfaces

We construct non-Lipshitz flow in $H^s$ for the cubic nonlinear Schrödinger 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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