Strichartz Estimates for Wave and Schrödinger Equations on Hyperbolic Trapped Domains

Strichartz estimates;Hyperbolic trapped domain;wave equations;Mathematics

Sun, HongtanSilverstone, Harris J. ;

Johns Hopkins University

关键词: Strichartz estimates;    Hyperbolic trapped domain;    wave equations;    Mathematics;   

Others  :  https://jscholarship.library.jhu.edu/bitstream/handle/1774.2/37854/SUN-DISSERTATION-2014.pdf?sequence=1&isAllowed=y

瑞士|英语

来源: JOHNS HOPKINS DSpace Repository

【 摘 要 】

In this thesis, I will establish the mixed norm Strichartz type estimates for thewave 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 hyperbolictrapped 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.