Blow-up and nonlinear instability for the magnetic Zakharov system

This study deals with the generalized Zakharov system with magnetic field. First of all, we construct a kind of blow-up solutions and establish the existence of blow-up solutions to the system through considering an elliptic system. Next, we show the nonlinear instability for a kind of periodic solutions. In addition, we consider the concentration properties of blow-up solutions for the system under study. At the end of this paper, we establish the global existence of weak solutions to the Cauchy problem of the system under consideration.