Non-Lipshitz flow of the nonlinear Schr\"odinger equation on surfaces

W. -M. Wang

Non-Lipshitz flow of the nonlinear Schr\"odinger equation on surfaces

Analysis of PDEs 2012-02-09 v1

Authors: W. -M. Wang

Abstract

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.

Keywords

nonlinear schr\"odinger equation non-lipshitz flow sobolev spaces 2-torus well-posedness cubic nonlinearity

Cite

@article{arxiv.1202.1638,
  title  = {Non-Lipshitz flow of the nonlinear Schr\"odinger equation on surfaces},
  author = {W. -M. Wang},
  journal= {arXiv preprint arXiv:1202.1638},
  year   = {2012}
}

Comments

7 pp, to appear in Forum Math

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