Strichartz Estimates for Wave and Schrödinger Equations on Hyperbolic Trapped Domains

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Johns Hopkins University
In this thesis, I will establish the mixed norm Strichartz type estimates for the wave and Schr odinger equations on certain Riemannian manifold. Here the manifold is the exterior domain of a smooth, normally hyperbolic trapped obstacle in n dimensional Euclidean space. I studied the case when n is greater than or equal to 3 and it is odd. As for the normally hyperbolic trapped obstacles, I got local Strichartz estimates for wave and Schr odinger equations with some loss of derivatives for the initial data. I also got a global Strichartz type estimates for the wave equation. In this case, I need two di erent LpLq mixed norms of the forcing term to bound the solution of the inhomogeneous equation.
Strichartz estimates, Hyperbolic trapped domain, wave equations