论文标题
临界非线性波方程的点衰变
Pointwise decay for the energy-critical nonlinear wave equation
论文作者
论文摘要
在这里列为\ cite {l}）的两部分系列中的第二篇文章（以下是[Arxiv：2105.02865]）证明了Quintic Defoce Quintic decodove equation的最佳角度衰减率，并在非机构空位上进行了大量初始数据，既有Quintic defocistic defocing defocing和Quintic Pocusing波动equequations contectime and quintic defoctic pocus a pove toperapers copting波波在少量初始数据spaciense and Nontystation space and nontystation space and spaceciens。我们证明了加权的局部能量衰减估计，并使用局部能量衰减和Strichartz对这些可变的背景进行了估计。通过使用迭代方案，我们获得了最佳的点界边界。此外，我们解释了迭代方案如何达到其他积分功率非线性的类似界限，鉴于这些力量的全球存在（鉴于某些初始衰减速率），该迭代方案的其他整体功率非线性是高于或低于Quintic功率的类似界限。
This second article in a two-part series (following [arXiv:2105.02865], listed here as \cite{L}) proves optimal pointwise decay rates for the quintic defocusing wave equation with large initial data on nonstationary spacetimes, and both the quintic defocusing and quintic focusing wave equations with small initial data on nonstationary spacetimes. We prove a weighted local energy decay estimate, and use local energy decay and Strichartz estimates on these variable-coefficient backgrounds. By using an iteration scheme, we obtain the optimal pointwise bounds. In addition, we explain how the iteration scheme reaches analogous pointwise bounds for other integral power nonlinearities that are either higher or lower than the quintic power, given the assumption of global existence for those powers (and in the case of the lower powers, given certain initial decay rates).
