Asymptotic behavior for solutions to the dissipative nonlinear Schrödinger equations with the fractional Sobolev space

Abstract

We study the Cauchy problem for the nonlinear Schrödinger equations with dissipative nonlinearity. In particular, we show the time decay estimate for global solutions in Lebesgue space of square integrable functions. Main results of this paper are the extension of results that have been proved in the work of Hayashi et al. [Adv. Math. Phys. 5, 3702738 (2016)].