A Generalized Representation Formula for Systems of Tensor Wave Equations

作者：Shao Arick^*

来源：Communications in Mathematical Physics, 2011, 306(1): 51-82.

DOI：10.1007/s00220-011-1273-2

In this paper, we generalize the Kirchhoff-Sobolev parametrix of Klainerman and Rodnianski (Hyperbolic Equ. 4(3):401-433, 2007) to systems of tensor wave equations with additional first-order terms. We also present a different derivation, which better highlights that such representation formulas are supported entirely on past null cones. This generalization of (Hyperbolic Equ. 4(3):401-433, 2007) is a key component for extending Klainerman and Rodnianski's breakdown criterion result for Einstein-vacuum spacetimes in (J. Amer. Math. Soc. 23(2):345-382, 2009) to Einstein-Maxwell and Einstein-Yang-Mills spacetimes.

• 出版日期2011-8