Local well-posedness for the $H^2$-critical nonlinear Schr\"odinger equation

Thierry Cazenave; Daoyuan Fang; Zheng Han

Local well-posedness for the $H^2$-critical nonlinear Schr\"odinger equation

Analysis of PDEs 2013-04-23 v1

Authors: Thierry Cazenave , Daoyuan Fang , Zheng Han

Abstract

In this paper, we consider the nonlinear Schr\"odinger equation $iu_t +\Delta u= \lambda |u|^{\frac {4} {N-4}} u$ in $\R^N$ , $N\ge 5$ , with $\lambda \in \C$ . We prove local well-posedness (local existence, unconditional uniqueness, continuous dependence) in the critical space $\dot H^2 (\R^N)$ .

Keywords

nonlinear schrödinger equation local well-posedness critical space h^2-critical unconditional uniqueness continuous dependence

Cite

@article{arxiv.1304.5564,
  title  = {Local well-posedness for the $H^2$-critical nonlinear Schr\"odinger equation},
  author = {Thierry Cazenave and Daoyuan Fang and Zheng Han},
  journal= {arXiv preprint arXiv:1304.5564},
  year   = {2013}
}

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