论文标题
在渐近平坦的时间上，Strauss型波系统解决方案的寿命
Lifespan of solutions to the Strauss type wave system on asymptotically flat space-times
论文作者
论文摘要
通过假设$（1+3）$ - 尺寸渐近时空的某些局部能量估计，我们研究了\ emph {strauss} type Wave系统的存在部分。首先，我们给出了一种与出现在\ cite {MR2944027}中的局部能量规范有关的时空估计。这些估计值可用于证明一系列加权\ emph {strichartz}和\ emph {kss}类型估计值，用于渐近平坦的时空上的波方程。然后，当非线性指数$ p $和$ q \ ge 2 $时，我们应用时空估算以获得寿命的下限。特别是，我们对亚临界案例的约束通常是尖锐的，我们将已知的$（p，q）$扩展到全球解决方案。此外，当$ p，q> 2 $时，不需要对初始数据紧凑。
By assuming certain local energy estimates on $(1+3)$-dimensional asymptotically flat space-time, we study the existence portion of the \emph{Strauss} type wave system. Firstly we give a kind of space-time estimates which are related to the local energy norm that appeared in \cite{MR2944027}. These estimates can be used to prove a series of weighted \emph{Strichartz} and \emph{KSS} type estimates, for wave equations on asymptotically flat space-time. Then we apply the space-time estimates to obtain the lower bound of the lifespan when the nonlinear exponents $p$ and $q\ge 2$. In particular, our bound for the subcritical case is sharp in general and we extend the known region of $(p,q)$ to admit global solutions. In addition, the initial data are not required to be compactly supported, when $p, q>2$.
