Non-Lipschitz flow of the nonlinear Schrodinger equation on surfaces

作者：Wang Wei Min^*

来源：Forum Mathematicum, 2013, 25(2): 221-227.

DOI：10.1515/FORM.2011.114

• Smooth metric
• Lipschitz-metric
• non-Lipschitz flow

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

• 出版日期2013-3