On the $L^{2}$-critical nonlinear Schrodinger equation with an inhomogeneous damping term

Abstract

We consider the $L^2$-critical nonlinear Schrodinger equation with an inhomogeneous damping term. We prove that there exists an initial data such that the corresponding solution is global in $H^1(R^d)$ and we give the minimal time of the blow up for some initial data.