Dispersion and Strichartz estimates for the Liouville equation |
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Authors: | Delphine Salort |
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Affiliation: | Université Paris 6, laboratoire Jacques-Louis Lions, UMR 7598, 175, rue du Chevaleret 75013 Paris, France |
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Abstract: | We consider the Liouville equation associated to a metric g and we prove dispersion and Strichartz estimates for the solution of this equation in terms of the geometry of the trajectories associated to g. In particular, we obtain global Strichartz estimates in time for metrics where dispersion estimate is false even locally in time. We also study the analogy between Strichartz estimates obtained for the Liouville equation and the Schrödinger equation with variable coefficients. To cite this article: D. Salort, C. R. Acad. Sci. Paris, Ser. I 342 (2006). |
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