Blowup for the Damped $L^{2}$-Critical Nonlinear Schrödinger Equation.

Mohamad Darwich (1)

1 LMPT - Laboratoire de Mathématiques et Physique Théorique

We consider the Cauchy problem for the $L^{2}$-critical damped nonlinear Schrödinger equation. We prove existence and stability of finite time blowup dynamics with the log-log blow-up speed for $\|\nabla u(t)\|_{L^2}$.

Domaines: Equations aux dérivées partielles [math.AP]

Mohamad Darwich. Blowup for the Damped $L^{2}$-Critical Nonlinear Schrödinger Equation.. Advances in Differential Equations, 2012, 17 (3-4), pp.337-367. ⟨hal-00558076⟩