论文标题
约束方程的高频解决方案
High-frequency solutions to the constraint equations
论文作者
论文摘要
我们通过求解$ \ Mathbb {r}^3 $上的约束方程，在维度3+1中为Einstein真空方程构建高频初始数据。我们的解决方案家庭$（\ bar {g}_λ，k_λ）_ {λ\ in（0,1]} $通过与几何光学方法相似的高频扩展来定义，并且在特定意义上与无效的灰尘数据相近。为了求解约束方程，我们使用了良好的挑战，以供您进行大量挑战，并以此为主要的挑战，以确保我们的范围挑战，我们的范围是我们的范围。本文的主要应用是我们的伴侣文章\ cite {touati2022a}，在该文章中，我们在广义波量表中构建高频引力波。
We construct high-frequency initial data for the Einstein vacuum equations in dimension 3+1 by solving the constraint equations on $\mathbb{R}^3$. Our family of solutions $(\bar{g}_λ,K_λ)_{λ\in(0,1]}$ is defined through a high-frequency expansion similar to the geometric optics approach and is close in a particular sense to the data of a null dust. In order to solve the constraint equations, we use their conformal formulation and the main challenge of our proof is to adapt this method in the high-frequency context. The main application of this article is our companion article \cite{Touati2022a} where we construct high-frequency gravitational waves in generalised wave gauge.
