Global existence of a nonlinear Schrodinger equation with viscous damping

In this note, we consider a Schrodinger evolution equation with a power nonlinearity i vertical bar u vertical bar(alpha)u and a viscous damping term nu Delta u. Then, we demonstrate that the Cauchy problem always admits the global existence of classical solutions with finite mass. Moreover, we can also observe that our proof is applicable for a nonlinear complex Ginzburg-Landau equation.