Solutions of quasi-linear wave equations polyhomogeneous at null infinity in high dimensions

Details Solutions of quasi-linear wave equations polyhomogeneous at null infinity in high dimensions Solutions of quasi-linear wave equations polyhomogeneous at null infinity in high dimensions

2010-10-12

arxiv.org/abs/1010.2387v1

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

88 pages, 3 figures

Scientific paper

We prove propagation of weighted Sobolev regularity for solutions of the hyperboloidal Cauchy problem for a class of quasi-linear symmetric hyperbolic systems, under structure conditions compatible with the Einstein-Maxwell equations in space-time dimensions $n+1\ge 7$. Similarly we prove propagation of polyhomogeneity in dimensions $n+1\ge 9$. As a byproduct we obtain, in those last dimensions, polyhomogeneity at null infinity of small data solutions of vacuum Einstein, or Einstein-Maxwell equations evolving out of initial data which are stationary outside of a ball.

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