Energy-critical NLS with quadratic potentials Killip, Rowan Visan, Monica Zhang, Xiaoyi We consider the defocusing H˙ 1-critical nonlinear Schr¨odinger equation in all dimensions (n ≥ 3) with a quadratic potential V (x) = ± 1/2|x|^2. We show global well-posedness for radial initial data obeying ∇u0(x), xu0(x) ∈L^2. In view of the potential V , this is the natural energy space. In the repulsive case, we also prove scattering. We follow the approach pioneered by Bourgain and Tao in the case of no potential; indeed, we include a proof of their results that incorporates a couple of simplifications discovered while treating the problem with quadratic potential. Informa UK Limited 2009 info:eu-repo/semantics/article doc-type:article text http://purl.org/coar/resource_type/c_2df8fbb1 https://research-explorer.ista.ac.at/record/22058 Killip R, Vişan M, Zhang X. Energy-critical NLS with quadratic potentials. <i>Communications in Partial Differential Equations</i>. 2009;34(12):1531-1565. doi:<a href="https://doi.org/10.1080/03605300903328109">10.1080/03605300903328109</a> eng info:eu-repo/semantics/altIdentifier/doi/10.1080/03605300903328109 info:eu-repo/semantics/altIdentifier/issn/0360-5302 info:eu-repo/semantics/altIdentifier/issn/1532-4133 info:eu-repo/semantics/altIdentifier/arxiv/math/0611394 info:eu-repo/semantics/openAccess