On the L²-critical nonlinear Schrödinger Equation with a nonlinear damping

2012/06/26 by Mohamad Darwich, Darwich, Mohamad
Mathematics · #Advanced Mathematical Physics Problems

paper · pdf · doi:10.48550/arxiv.1206.6082

Abstract

We consider the Cauchy problem for the L²-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 ‖∇ u(t)‖_L².

Citations

• Uniqueness of positive solutions of Δu−u+up=0 in Rn

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