论文标题
vaidya时空上波方程的剥离行为
Peeling-off behaviour of the wave equation on the Vaidya spacetime
论文作者
论文摘要
我们研究了Mason and Nicolas在Mason-Nicolas 2009中开发的Vaidya时空上的波方程的剥离。其想法是在恢复现场的零无穷大属性下的规律性，其特征在于Sobolev-Type Narms的特征，其在初始数据的相应功能方面。所有功能空间都是从与Minkowski时空上Morawetz Vector场构建的观察者相关的能量通量获得的。我们结合了共形技术和能量估计，以获得最佳的初始数据类别，以确保给定的重新定期。数据类别等于在Minkowski和Schwarzschild的空间上获得的数据，因为它们在无穷大和规律性下施加了相同的衰变。
We study the peeling for the wave equation on the Vaidya spacetime following the approach developed by Mason and Nicolas in Mason-Nicolas 2009. The idea is to encode the regularity at null infinity of the rescaled field, characterised by Sobolev-type norms, in terms of corresponding function spaces of initial data. All function spaces are obtained from energy fluxes associated with an observer constructed from the Morawetz vector field on Minkowski spacetime. We combine conformal techniques and energy estimates to obtain the optimal classes of initial data ensuring a given regularity of the rescaled field. The classes of data are equivalent with those obtained on Minkowski and Schwarzschild spacetimes in that they impose the same decay at infinity and regularity.
