Strichartz estimates and the nonlinear Schrödinger equation on manifolds with boundary

Autor: Christopher D. Sogge, Matthew D. Blair, Hart F. Smith
Rok vydání: 2011
Předmět:
Zdroj: Mathematische Annalen. 354:1397-1430
ISSN: 1432-1807
0025-5831
Popis: We establish Strichartz estimates for the Schrodinger equation on Riemannian manifolds (Ω, g) with boundary, for both the compact case and the case that Ω is the exterior of a smooth, non-trapping obstacle in Euclidean space. The estimates for exterior domains are scale invariant; the range of Lebesgue exponents (p, q) for which we obtain these estimates is smaller than the range known for Euclidean space, but includes the key $${L^{4}_{t}L^{\infty}_x}$$ estimate, which we use to give a simple proof of well-posedness results for the energy critical Schrodinger equation in 3 dimensions. Our estimates on compact manifolds involve a loss of derivatives with respect to the scale invariant index. We use these to establish well-posedness for finite energy data of certain semilinear Schrodinger equations on general compact manifolds with boundary.
Databáze: OpenAIRE
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