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Energy-Critical NLS with Quadratic Potentials

Energy-Critical NLS with Quadratic Potentials

We consider the defocusing -critical nonlinear Schrödinger equation in all dimensions (n ≥ 3) with a quadratic potential . We show global well-posedness for radial initial data obeying ∇u 0(x), xu 0(x) ∊ L 2. In view of the potential V, this is the natural energy space. In the repulsive …