Existence and nonexistence of global solutions for time-dependent damped NLS equations

Abstract

We investigate the Cauchy problem for the nonlinear Schrödinger equation with a time-dependent linear damping term. Under non standard assumptions on the loss dissipation, we prove the blow-up in the inter-critical regime, and the global existence in the energy subcritical case. Our results generalize and improve the ones in [9, 11, 21].

To appear in Communications on Pure and Applied Analysis