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On the global
well-posedness of energy-critical Schrödinger equations in
curved spaces
Alexandru D. Ionescu, Benoit Pausader and Gigliola Staffilani |
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Vol. 5 (2012), No. 4, 705–746
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Abstract |
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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 . |
Keywords
global well-posedness, energy-critical defocusing NLS,
nonlinear Schrödinger equation, induction on energy
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Mathematical Subject Classification 2000
Primary: 35Q55
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Milestones
Received: 5 August 2010
Accepted: 1 April 2011
Published: 27 November 2012
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Authors |
| Alexandru D. Ionescu | |
| Department of Mathematics Princeton University Washington Road Princeton, NJ 08544 United States |
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| Benoit Pausader | |
| Department of Mathematics Brown University 151 Thayer Street Providence, RI 02912 United States |
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| Gigliola Staffilani | |
| Department of Mathematics Massachusetts Institue of Technology 77 Massachusetts Avenue, 2-246 Cambridge, MA 02139 United States |
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