Quintic NLS in the exterior of a strictly convex obstacle

Abstract

We consider the defocusing energy-critical nonlinear Schrödinger equation in the exterior of a smooth compact strictly convex obstacle in three dimensions. For the initial-value problem with Dirichlet boundary condition we prove global well-posedness and scattering for all initial data in the energy space.

arXiv comment116 pages, 5 figures

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• Riesz transforms outside a convex obstacle
• The focusing cubic NLS on exterior domains in three dimensions
• On 2D NLS on non-trapping exterior domains