Non-Lipshitz flow of the nonlinear Schrödinger equation on surfaces

Details Non-Lipshitz flow of the nonlinear Schrödinger equation on surfaces Non-Lipshitz flow of the nonlinear Schrödinger equation on surfaces

2012-02-08

arxiv.org/abs/1202.1638v1

Mathematics

Analysis of PDEs

7 pp, to appear in Forum Math

Scientific paper

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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