Concerning the Klein-Gordon equation on asymptotically Euclidean manifolds

asymptotically;KSS;energy decay;phase method;Mathematics

Xue, MinSogge, Christopher D. ;

Johns Hopkins University

关键词: asymptotically;    KSS;    energy decay;    phase method;    Mathematics;   

Others  :  https://jscholarship.library.jhu.edu/bitstream/handle/1774.2/39549/XUE-DISSERTATION-2015.pdf?sequence=1&isAllowed=y

瑞士|英语

来源: JOHNS HOPKINS DSpace Repository

【 摘 要 】

The aim of the dissertation is to study the Klein-Gordon equation on asymptotically Euclidean manifolds. Using Mourre estimates, we obtain KSS estimates for the Klein-Gordon equation on (R^d, g), when metric g is non-trapping and approaches the Euclidean metric like ^{-ho}. Together with local energy decay, we can obtain the Strichartz estimate for compact perturbation metric. Also, using stationary phase methods and parametric constructions, we can obtain the dispersive estimate which implies the global Strichartz estimates for non-compact small perturbation.