Non-Lipshitz flow of the nonlinear Schrödinger equation on surfaces

Abstract

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.

7 pp, to appear in Forum Math

References in corpus (1)

• Supercritical Nonlinear Schrödinger Equations II: Almost Global Existence