Nonexistence of Global Solutions to the Cauchy Problem for the Damped Nonlinear Schrödinger Equations

Abstract

Solutions to the Cauchy problem for the equation $iu_t = \Delta + (\left| u \right|^2 )u - ({{ia} / 2})u\,(a > 0,x \in R^n ,t > 0);\,u(x,0) = u_0 (x)$ are considered. Conditions on uo and q are given so that solutions do not exist for all $t > 0$