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Blow-up, global existence and standing waves for the magnetic nonlinear Schrödinger equations

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  • We study blow-up, global existence and standing waves for the nonlinear Schrödinger equations with two-dimensional magnetic field in a cold plasma. Under certain conditions on initial data and initial energy, we derive finite time blow-up phenomena of the solutions to the equations under study. Using compactness and Lagrange multiplier method, we establish the existence of standing waves. Finally, by introducing invariant manifolds and utilizing potential well argument as well as concavity method, we obtain the sharp threshold for global existence and blowup.
    Mathematics Subject Classification: Primary: 35A15, 35B30; Secondary: 35Q55.

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