Energy Critical NLS in two space dimensions
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🧮 math.AP
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criticalenergyregimesspacesubcriticalsupercriticalwell-posednesscase
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We investigate the initial value problem for a defocusing nonlinear Schr\"odingerequation with exponential nonlinearity. We identify subcritical, critical and supercritical regimes in the energy space. We establish global well-posedness in the subcritical and critical regimes. Well-posedness fails to hold in the supercritical case.
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