| 摘 要： | In this paper, the auther considers following initial value problem for the system of nonlinear Schrodinger equation with the magnetic field effect
$i\varepsilon _i-\Delta \varepsilon +\beta q(|\varepsilon |^2)\varepsilon +\eta \varepsilon \times (\varepsilon \times \varepsilon )=0$(1.1)
$\varepsilon |t=0=\varepsilon _0(x),x\in R^2,$(1.2)
where\beta,\eta are real constants, \varepsilon = (\varepsilon ^1, \varepsilon ^2, \varepsilon ^3). First, the existence of the global solution for problem (1.1), (1.2) is established by means of the method of integral estimates, and then the “blow up” theorem is obtained nuder some conditions.
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