论文标题
e（1）问题的散射
Scattering for the Equivariant U(1) Problem
论文作者
论文摘要
为$ 2+1 $ einstein-wave地图系统扩展了我们先前在凯奇问题上的工作，我们证明，线性部分占主导地位的波浪图方程的非线性部分，该部分耦合到整个爱因斯坦方程组，用于小数据。证明中的关键要素是完全耦合的爱因斯坦波映射的非线性摩拉维兹估计值。 $ 2+1 $尺寸爱因斯坦波地图系统自然发生在U（1）对称$ 3+1 $尺寸真空爱因斯坦方程的一般相对论。
Extending our previous works on the Cauchy problem for the $2+1$ equivariant Einstein-wave map system, we prove that the linear part dominates the nonlinear part of the wave maps equation coupled to the full set of the Einstein equations, for small data. A key ingredient in the proof is a nonlinear Morawetz estimate for the fully coupled equivariant Einstein-wave maps. The $2+1$ dimensional Einstein-wave map system occurs naturally in the U(1) symmetric $3+1$ dimensional vacuum Einstein equations of general relativity.
