Gevrey-modulation spaces and smoothing effect for the system of nonlinear Schrödinger equations

Abstract

We study the Cauchy problem for the system of nonlinear Schrodinger equations under the mass resonance condition. In particular, we show the Gevrey smoothing effect for the global solutions with data which satisfy the sub-exponentially decaying condition and have sufficiently small norm under the scale critical setting of $$L^2$$. Furthermore, we show the existence of final states for solutions and the time decay estimates in the Gevrey-modulation spaces. Also we treat the same result to the above result in the framework of usual modulation spaces.