论文标题
在退化情况下的径向线性化能量临界波方程的能量通道上
On channels of energy for the radial linearised energy critical wave equation in the degenerate case
论文作者
论文摘要
能量估计的通道控制了初始数据的能量，从而从光锥外辐射的能量。对于线性化的能量临界波方程，它们是在径向情况下以奇数尺寸获得的，首先是Duyckaerts，Kenig和Merle的$ 3 $维度（Camb。J.Math。，2013年），然后是同一作者的一般奇数（Comm。Math。Phys。，2020）。我们考虑的甚至尺寸，为此，已知这种估计失败（Côte，Kenig和Schlag，Math。Ann。，2014年）。我们提出了这些估计值的较弱版本，围绕单个基础状态以及多层面。这使我们能够在六个维度（Collot，Duyckaerts，Kenig和Merle，Arxiv Preprint 2201.01848，2022版本1和2）中证明孤子分辨率的猜想。
Channels of energy estimates control the energy of an initial data from that which it radiates outside a light cone. For the linearised energy critical wave equation they have been obtained in the radial case in odd dimensions, first in $3$ dimensions by Duyckaerts, Kenig and Merle (Camb. J. Math., 2013), then for general odd dimensions by the same authors (Comm. Math. Phys., 2020). We consider even dimensions, for which such estimates are known to fail (Côte, Kenig and Schlag, Math. Ann., 2014). We propose a weaker version of these estimates, around a single ground state as well as around a multisoliton. This allows us to prove the soliton resolution conjecture in six dimensions (Collot, Duyckaerts, Kenig and Merle, arXiv preprint 2201.01848, 2022 versions 1 and 2).
