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 …