Some remarks on the nonlinear Schrödinger equation with fractional dissipation
Some remarks on the nonlinear Schrödinger equation with fractional dissipation
We consider the Cauchy problem for the L2-critical focussing 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 ∇u(t)L2.