Some Results for a Class of Nonlinear Schrödinger Equations With Derivative Nonlinearities

ABSTRACT In this paper, we consider a class of nonlinear Schrödinger equations with derivative nonlinearities, which is first introduced by Colin and Colin [ Differential Integral Equations 17 (2004): 297–330] as a model of laser‐plasma interaction. Based on concentration‐compactness principle combined with variational methods, we prove some existence and nonexistence results of normalized ground states, respectively. Furthermore, we obtain the global well‐posedness in three‐dimensional space. By using conservation laws and Virial estimate, we also investigate some blow‐up results.