论文标题
渐近的波动方程的局部能量估计在接近Kerr的局部能量估计
A local energy estimate for wave equations on metrics asymptotically close to Kerr
论文作者
论文摘要
在本文中，我们证明了对具有小角动量的KERR度量的慢速衰减指标的线性波方程的局部能量估计。作为应用程序，我们研究quasilinear Wave方程$ \ box_ {g（u，t，x）} u = 0 $ 指标$ g（u，t，x）$与带有小角动量$ g（0，t，x）$的kerr公制的近距离（渐近等于）。根据公制的合适假设 系数，并假设$ u $的初始数据足够小，我们证明了解决方案$ u $的全球存在和衰减。
In this article we prove a local energy estimate for the linear wave equation on metrics with slow decay to a Kerr metric with small angular momentum. As an application, we study the quasilinear wave equation $\Box_{g(u, t, x)} u = 0$ where the metric $g(u, t, x)$ is close (and asymptotically equal)to a Kerr metric with small angular momentum $g(0,t,x)$. Under suitable assumptions on the metric coefficients, and assuming that the initial data for $u$ is small enough, we prove global existence and decay of the solution $u$.
