This paper studies a class of nonlocal nonlinear Schr¨odinger equations in R3, which occurs in the infinite ion acoustic speed limit of the Zakharov system with magnetic fields in a cold plasma. The magnetic fields induce some nonlocal effects in these nonlinear Schr¨odinger systems, and the main goal of this paper is to understand these effects. The key is to establish some a priori estimates on those nonlocal terms generated by the magnetic field, through which we obtain various conclusions including finite time blow-ups, sharp threshold of global existence and instability of standing waves for these equations.
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