Strichartz estimates and nonlinear wave equation on nontrapping asymptotically conic manifolds

被引：14
作者：
Zhang, Junyong [1 ,2 ]
机构：
[1] Beijing Inst Technol, Dept Math, Beijing 100081, Peoples R China
[2] Australian Natl Univ, Dept Math, Canberra, ACT 0200, Australia
来源：
ADVANCES IN MATHEMATICS | 2015年 / 271卷
基金：
中国国家自然科学基金; 澳大利亚研究理事会; 北京市自然科学基金;
关键词：
Strichartz estimate; Asymptotically conic manifold; Spectral measure; Global existence; Scattering theory; HEAT KERNEL; SCATTERING; PROPAGATOR; EXISTENCE; RESOLVENT;
D O I：
10.1016/j.aim.2014.11.013
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We prove the global-in-time Strichartz estimates for wave equations on the nontrapping asymptotically conic manifolds. We obtain estimates for the full set of wave admissible indices, including the endpoint. The key points are the properties of the microlocalized spectral measure of Laplacian on this setting showed in [18] and a Littlewood-Paley squarefunction estimate. As applications, we prove the global existence and scattering for a family of nonlinear wave equations on this setting. (C) 2014 Elsevier Inc. All rights reserved.
引用
收藏
页码：91 / 111
页数：21
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