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Solutions of Quasi-linear Wave Equations Polyhomogeneous at Null Infinity in High Dimensions by Chruściel, Piotr T.; Wafo, Roger Tagne is a scholarly article available to read on EtoBox.

What is Solutions of Quasi-linear Wave Equations Polyhomogeneous at Null Infinity in High Dimensions about?

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.

Author

Chruściel, Piotr T.; Wafo, Roger Tagne

Published

2010

Language

EN