Local well-posedness of the nonlinear Schr\"odinger equations on the sphere for data in modulation spaces

Hideo Takaoka

Local well-posedness of the nonlinear Schr\"odinger equations on the sphere for data in modulation spaces

Analysis of PDEs 2015-02-17 v1

Authors: Hideo Takaoka

Abstract

In this paper we discuss a priori estimates derived from the energy method to the initial value problem for the cubic nonlinear Schr\"odinger on the sphere $S^2$ . Exploring suitable a priori estimates, we prove the existence of solution for data whose regularity is $s=1/4$ .

Keywords

nonlinear Schrödinger equation sphere modulation space local well-posedness a priori estimate initial value problem cubic nonlinearity

Cite

@article{arxiv.1502.04283,
  title  = {Local well-posedness of the nonlinear Schr\"odinger equations on the sphere for data in modulation spaces},
  author = {Hideo Takaoka},
  journal= {arXiv preprint arXiv:1502.04283},
  year   = {2015}
}

Comments

17 pages

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