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|Abstract:||In this paper we present a method to study global regularity properties of solutions of large-data critical Schrodinger 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 H-1 for the energy-critical defocusing initial-value problem (i partial derivative(t) + Delta(g))u = u vertical bar u vertical bar(4), u(0) = phi, on hyperbolic space H-3.|
|Electronic Publication Date:||27-Nov-2012|
|Citation:||Ionescu, Alexandru D, Pausader, Benoit, Staffilani, Gigliola. (2012). ON THE GLOBAL WELL-POSEDNESS OF ENERGY-CRITICAL SCHRODINGER EQUATIONS IN CURVED SPACES. ANALYSIS & PDE, 5 (705 - 746. doi:10.2140/apde.2012.5.705|
|Pages:||705 - 746|
|Type of Material:||Journal Article|
|Journal/Proceeding Title:||ANALYSIS & PDE|
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