THE GLOBAL SOLUTION AND“BLOW UPPHENOMENON FOR A CLASS OF SYSTEM OF NONLINEAR SCHR（?）DINGER EQUATIONS WITH THE MAGNETIC FIELD EFFECT

摘要

＜正＞ In this paper,the auther considers following initial value problem for the system ofnonlinear Schrdinger equation with the magnetic field effectiεt-△ε+βq（丨ε丨~2）ε+ηε×（ε×ε）=0 （1.1）ε丨t0=ε0（x）,x∈R~2,（1.2）where β,η are real constants,ε=（ε~1,ε~2,ε~3）.First,the existence of the global solutionfor problem（1.1）,（1.2）is established by means of the method of integral estimates,andthen the “blow up” theorem is obtained nuder some conditions.