Abstract
In this paper we present a method to study global regularity properties of solutions of large-data critical Schrödinger equations on certain noncompact Riemannian manifolds. We rely on concentration compactness arguments and a global Morawetz inequality adapted to the geometry of the manifold (in other words we adapt the method of Kenig and Merle to the variable coefficient case), and a good understanding of the corresponding Euclidean problem (a theorem of Colliander, Keel, Staffilani, Takaoka and Tao).
As an application we prove global well-posedness and scattering in for the energy-critical defocusing initial-value problem
on hyperbolic space .
Citation
Alexandru Ionescu. Benoit Pausader. Gigliola Staffilani. "On the global well-posedness of energy-critical Schrödinger equations in curved spaces." Anal. PDE 5 (4) 705 - 746, 2012. https://doi.org/10.2140/apde.2012.5.705
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