Abstract: In terms of the characteristics of the ground state, a sharp condition for blowup and global existence of the generalized Davey-Stewartson system in three dimensional spaces is derived out by applying the potential well argument and the concavity method. Meanwhile, that how small the initial data are, the existence of the global solution is also shown

Key words: Sharp condition, Generalized Davey-Stewartson system, Global existence, Blowup, Ground state