In this paper, we consider the Cauchy problem of SchrÖdinger-IMBq equations in ℝn, n ≥ 1. We first show the global existence and blowup criterion of solutions in the energy space for the 3 and 4 dimensional system without power nonlinearity under suitable smallness assumption. Secondly the global existence is established to the system with p-powered nonlinearity in Hs (ℝn), n = 1, 2 for some n/2 < s < min(2, p) and some p > n/2. We also provide a blowup criterion for n = 3 in Triebel-Lizorkin space containing BMO space naturally.
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