Harmonic Analysis
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The Cauchy problem for the nonlinear Schrödinger equation on compact manifolds
speaker: Patrick Gérard (Université Paris-Sud, Laboratoire de Mathématiques d'Orsay)abstract: This minicourse will be devoted to some phase space methods used in the study of the Cauchy problem for the nonlinear Schrodinger equation on Rie mannian compact manifolds of dimension 2 or 3. In the first part the link between WKB method, dispersion e#ects and Strichartz estimates will be discussed, with applications to global existence for NLS on general compact manifolds. In the second part these results will be improved on specific mani folds such as spheres ; the main tools in this case will be multilinear estimates of eigenfunctions, combined with analysis in conormal Bourgain spaces.
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