We investigate the initial value problem for a defocusing nonlinear Schrödinger equation with exponential nonlinearity i∂tu + Δu = u(e4π u 2 - 1) in ℝt × ℝx 2. 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.
- Energy critical
- Nonlinear Schrödinger equation
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