On the $L^2$-critical nonlinear Schrödinger Equation with a nonlinear damping

Mohamad Darwich

doi:10.3934/cpaa.2014.13.2377

Article Contents

2014, Volume 13, Issue 6: 2377-2394. Doi: 10.3934/cpaa.2014.13.2377

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On the $L^2$-critical nonlinear Schrödinger Equation with a nonlinear damping

Mohamad Darwich^1,

1.
Laboratoire de Mathématiques et Physique Théorique, UMR 7350, Tours

Received: September 30, 2013

Revised: April 30, 2014

Published: October 2014

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Abstract

We consider the Cauchy problem for the $L^2$-critical nonlinear Schrödinger 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:

Shrödinger equations,
PDE's.

Mathematics Subject Classification: Primary: 35M11; Secondary: 35A01.

Citation:

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