PORTUGALIAE MATHEMATICA Vol. 62, No. 3, pp. 349370 (2005) 

Shock waves and gravitational waves in matter spacetimes with Gowdy symmetryP.G. LeFloch and J.M. StewartLaboratoire JacquesLouis Lions & Centre National de la Recherche Scientifique, UMR 7598,Université Pierre et Marie Curie, B.C. 187, 75252 Paris Cedex 05  FRANCE Email: lefloch@ann.jussieu.fr Department of Applied Mathematics and Theoretical Physics, Centre for Mathematical Sciences, Cambridge CB3 0WA  UK Email: j.m.stewart@damtp.cam.ac.uk Abstract: In the context of classical general relativity, we consider the matter Einstein equations for perfect fluids on Gowdy spacetimes with planesymmetry. Such spacetimes admit two commuting Killing vector fields and contain gravitational waves; the fluid variable may exhibit shock waves. We establish the existence of a bounded variation solution to the Cauchy problem, which is defined globally until either a true singularity occurs in the geometry (e.g. the vanishing of the area of the $2$dimensional spacelike orbits of the symmetry group) or a blowup of the energy density takes place. Keywords: EinsteinEuler equations; Gowdy spacetimes; singularities; hyperbolic equations; conservation laws; shock waves; compensated compactness. Classification (MSC2000): 83C05, 83C35, 76L05, 35L65. Full text of the article:
Electronic version published on: 7 Mar 2008.
© 2005 Sociedade Portuguesa de Matemática
