Global Well-Posedness and Analytic Smoothing Effect for the Dissipative Nonlinear Schroedinger Equations

摘要

We study the global Cauchy problem for the nonlinear Schrodinger equations in the Sobolev space of fractional order. In particular, we show the global well-posedness and the analytic smoothing effect for global solutions to a dissipative nonlinear Schrodinger equation for large data by applying a priori estimate in the Sobolev space of fractional order.