Sharp Thresholds of Blowup and Global Existence for System of Nonlinear Schrdinger Equation under a Potential

The blow-up and global existence concerning solutions of nonlinear Schrdinger equation is put under examination in N-dimensional Euclidean space. What we discuss about here are largely some developments of our predecessors’ findings in this regard. By use of variation and construction of invariant manifold, the sharp threshhold for blowup and global existence of the solution are thus obtained.