首页 | 本学科首页   官方微博 | 高级检索  
     


Strichartz estimates in the hyperbolic space and global existence for the semilinear wave equation
Authors:Daniel Tataru
Affiliation:Department of Mathematics, Princeton University, Princeton, New Jersey 08540
Abstract:

The aim of this article is twofold. First we consider the wave equation in the hyperbolic space $mathbb H^n$ and obtain the counterparts of the Strichartz type estimates in this context. Next we examine the relationship between semilinear hyperbolic equations in the Minkowski space and in the hyperbolic space. This leads to a simple proof of the recent result of Georgiev, Lindblad and Sogge on global existence for solutions to semilinear hyperbolic problems with small data. Shifting the space-time Strichartz estimates from the hyperbolic space to the Minkowski space yields weighted Strichartz estimates in $mathbb R^{n} times mathbb R$ which extend the ones of Georgiev, Lindblad, and Sogge.

Keywords:Semilinear wave equation   Strichartz estimates   hyperbolic space
点击此处可从《Transactions of the American Mathematical Society》浏览原始摘要信息
点击此处可从《Transactions of the American Mathematical Society》下载全文
设为首页 | 免责声明 | 关于勤云 | 加入收藏

Copyright©北京勤云科技发展有限公司  京ICP备09084417号