Strichartz estimates in the hyperbolic space and global existence for the semilinear wave equation
Strichartz estimates in the hyperbolic space and global existence for the semilinear wave equation
复制标题
DOI：
10.1090/s0002-9947-00-02750-1
复制
发表时间：
2000-10
影响因子：
1.3
通讯作者：
D. Tataru
中科院分区：
文献类型：
--
作者：
D. Tataru
本文的目的有两个。首先，我们考虑了双曲空间HI中的波动方程，得到了相应的Strichartz估计。接下来，我们研究Minkowski空间和双曲空间中的半线性双曲型方程之间的关系。这简单地证明了Georgiev，Lindblad和Sogge关于小数据半线性双曲型问题解的整体存在性的最新结果。将时空Strichartz估计从双曲空间移动到Minkowski空间得到了Rn×1R的加权Strichartz估计，它推广了Georgiev，Lindblad和Sogge的估计。
The aim of this article is twofold. First we consider the wave equation in the hyperbolic space HI 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 Rn x 1R which extend the ones of Georgiev, Lindblad, and Sogge.