Existence and finite time blow-up for nonlinear Schrödinger equations in the Bopp-Podolsky electrodynamics

Abstract

In this paper, we consider the nonlinear Schrödinger equations in the Bopp-Podolsky electrodynamics. By using the fixed point theorem and the method of Strichartz's estimate, we construct local solutions in some spatial-time space and further prove global existence result for small data. Moreover, we establish the virial identity for the system and show that solutions with negative energy blow up in finite time.