Shock waves in self-gravitating fluids
The theory of shock waves deals with discontinuous solutions of certain
equations such as the Euler equations of a perfect fluid. If a fluid is chosen
as matter model in general relativity then shock waves are likely to be
encountered. At least that is the intuition. Recently Fredrik Ståhl and
I were are to turn this into a theorem.
(Cf. arXiv:0806.1597.)
It gives a rigorous proof that
under certain conditions shock waves evolve from regular initial configurations
in self-gravitating fluids in general relativity. In addition some qualitative
information is obtained about the process of formation of the shock. A natural
next step is to develop techniques which allow existence of solutions beyond
the shocks to be proved. This has been done in recent work together with
Philippe LeFloch where we have obtained results which are global in time.
(Cf. arXiv:1004.0427.)
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Alan Rendall
Last modified: Fri May 16 11:07:29 MESZ 2003