On the low-regularity global well-posedness of a system of nonlinear Schrodinger Equation

Abstract

In this article, we study the low-regularity Cauchy problem of a one dimensional quadratic Schrodinger system with coupled parameter α ∈ (0, 1). When 1 2 < α < 1, we prove the global well-posedness in H s with s > − 1 4 , while for 0 < α < 1 2 , we obtain global well-posedness in H s with s > − 5 8 . We have adapted the linear-nonlinear decomposition and resonance decomposition technique in different ranges of α