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

Author(s)
Piotr T. Chrusciel, Roger Tagne Wafo
Abstract

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 >= 7. Similarly we prove propagation of polyhomogeneity in dimensions n + 1 >= 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.

Organisation(s)
Gravitational Physics
External organisation(s)
University of Douala
Journal
Journal of Hyperbolic Differential Equations
Volume
8
Pages
269-346
No. of pages
78
ISSN
0219-8916
DOI
https://doi.org/10.1142/S0219891611002445
Publication date
2011
Peer reviewed
Yes
Austrian Fields of Science 2012
103036 Theoretical physics, 103028 Theory of relativity, 103019 Mathematical physics
Portal url
https://ucris.univie.ac.at/portal/en/publications/solutions-of-quasilinear-wave-equations-polyhomogeneous-at-null-infinity-in-high-dimensions(819f9c5c-e07a-4831-84e2-e8d959068085).html