Blow-Up Of Solutions For A Class Of Nonlinear Schr(?)dinger System

In this paper, we consider the blow-up of L2-solutions for the following nonlinear Schrodinger system,The above system can be equivalently changed into the following integral system:First, we obtain the local existence of solutions of the integral system by a fixed point technique.Then we prove the solution of the integral system is a weak solution of the above system by introducing appropriate function sequence and changing variables and mainly using the Strichartz estimate and Holder inequality.Finally, we give the nonexistence of non-trivial global weak solutions of above equations by test-functions method, and we only obtain the trivial solutions by esti-mating the limit of two appropriate positive functions.This paper shows that the existence of the blow-up solutions is determinated by the sign of the initial data integral, but not related to its norm,namely, the L2-norm of solutions of above system can blow up,even if the data is sufficiently small,where 1<p2≤p1≤1+2/n.