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

Mohamad Darwich (1)

1 LMPT - Laboratoire de Mathématiques et Physique Théorique

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 $\|\nabla u(t)\|_{L^2}$.

Domains: Analysis of PDEs [math.AP]

Mohamad Darwich. On the $L^{2}$-critical nonlinear Schrödinger Equation with a nonlinear damping.. 2013. ⟨hal-00712285v4⟩