不定常非俘获背景下标量场的局域能量衰减
Local energy decay for scalar fields on time dependent non-trapping backgrounds
摘要：
考虑非俘获渐近平坦空间-时间上标量波方程解的局部能量衰减估计。我们的目标是双重的。首先，我们考虑平稳的情况下，我们可以提供一个完整的局部能量衰减边界的谱表征，这种表征简化了平稳对称的情况下。然后，我们考虑几乎平稳，几乎对称的情况。在那里，我们建立了两个主要的结果：第一个是“两点”当地的能量衰减估计是有效的一般类（非对称）几乎驻波方程，满足一定的非共振性质在零频率。第二个结果，这也需要几乎对称的条件，是建立一个指数剖分的能量空间通过有限维不定常稳定和不稳定的子空间，与无限维的补充，解决方案分散通过通常的本地能量衰减估计。
英文摘要：
We consider local energy decay estimates for solutions to scalar wave equations on nontrapping asymptotically flat space-times. Our goals are two-fold. First we consider the stationary case, where we can provide a full spectral characterization of local energy decay bounds; this characterization simplifies in the stationary symmetric case. Then we consider the almost stationary, almost symmetric case. There we establish two main results: The first is a "two point" local energy decay estimate which is valid for a general class of (non-symmetric) almost stationary wave equations which satisfy a certain nonresonance property at zero frequency. The second result, which also requires the almost symmetry condition, is to establish an exponential trichotomy in the energy space via finite dimensional time dependent stable and unstable sub-spaces, with an infinite dimensional complement on which solutions disperse via the usual local energy decay estimate.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
