Asymptotic behavior for a class of derivative nonlinear Schrödinger systems

We consider the initial value problem for systems of derivative nonlinear Schrödinger equations with nonlinearity of the critical power in one and two space dimensions. Li–Sunagawa and Sakoda–Sunagawa introduced a sufficient condition, which is weaker than the so-called null condition, for the small data global existence of solutions. In this paper, we investigate the asymptotic behavior of global solutions under a condition related to the above one.