Some remarks on the nonlinear Schrödinger equation with fractional dissipation

Abstract

We consider the Cauchy problem for the $L^2$-critical nonlinear Schrödinger equation with a fractional dissipation. According to the order of the fractional dissipation, we prove the global existence or the existence of finite time blowup dynamics with the log-log blow-up speed for $\Vert \nabla u(t){\Vert }_{L^2}$.

arXiv commentarXiv admin note: text overlap with arXiv:1206.6082

References in corpus (1)

• Nonlinear-damping continuation of the nonlinear Schrödinger equation - a numerical study