Some remarks on the nonlinear Schr\"odinger equation with fractional dissipation

Mohamad Darwich; Luc Molinet

Some remarks on the nonlinear Schr\"odinger equation with fractional dissipation

Analysis of PDEs 2016-10-07 v1

Authors: Mohamad Darwich , Luc Molinet

Abstract

We consider the Cauchy problem for the $L^2$ -critical nonlinear Schr\"odinger equation with a fractional dissipation. According to the order of the fractional dissipation, we prove the global existence or the existence of finite time blowup dynamics with the log-log blow-up speed for $\|\nabla u(t)\|_{L^2}$ .

Keywords

nonlinear Schrödinger equation fractional dissipation Cauchy problem global existence finite time blowup log-log blow-up speed L^2-critical

Cite

@article{arxiv.1511.08577,
  title  = {Some remarks on the nonlinear Schr\"odinger equation with fractional dissipation},
  author = {Mohamad Darwich and Luc Molinet},
  journal= {arXiv preprint arXiv:1511.08577},
  year   = {2016}
}

Comments

arXiv admin note: text overlap with arXiv:1206.6082

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