Space-Time Analytic Smoothing Effect for Global Solutions to a System of Nonlinear Schrödinger Equations with Large Data

Abstract

We study the Cauchy problem for a quadratic system of nonlinear Schrodinger equations in $$L^2$$ -setting with the space dimension $$n=1,2$$ or 3. Recently, the author showed that the local solution for the system of nonlinear Schrodinger equations has space-time analytic smoothing effect for data with exponentially weighted $$L^2$$ -norm. Also as is well known, the quadratic nonlinear Schrodinger equations have global solutions in $$L^2$$ -subcritical setting. Our main purpose of this study is to show real analyticity in both space and time variables of the unique global solution with data which has large exponentially weighted $$L^2$$ -norm.