On the $L^{2}$-critical nonlinear Schr\"odinger Equation with a nonlinear damping

Mohamad Darwich

On the $L^{2}$-critical nonlinear Schr\"odinger Equation with a nonlinear damping

Analysis of PDEs 2013-01-16 v4

Authors: Mohamad Darwich

Abstract

We consider the Cauchy problem for the $L^{2}$ -critical nonlinear Schr\"{o}dinger equation with a nonlinear damping. According to the power of the damping term, 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 L^2-critical nonlinear damping blowup dynamics global existence

Cite

@article{arxiv.1206.6082,
  title  = {On the $L^{2}$-critical nonlinear Schr\"odinger Equation with a nonlinear damping},
  author = {Mohamad Darwich},
  journal= {arXiv preprint arXiv:1206.6082},
  year   = {2013}
}

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