RT Journal Article
T1 Well-posedness of the Einstein-Euler system in asymptotically flat spacetimes: The constraint equations
A1 Brauer, Uwe Richard Otto
A1 Karp, Lavi
AB This paper deals with the construction of initial data for the coupled Einstein-Euler system. We consider the condition where the energy density might vanish or tend to zero at infinity, and where the pressure is a fractional power of the energy density. In order to achieve our goals we use a type of weighted Sobolev space of fractional order. The common Lichnerowicz-York scaling method (Choquet-Bruhat and York, 1980 [9]; Cantor, 1979 [7]) for solving the constraint equations cannot be applied here directly. The basic problem is that the matter sources are scaled conformally and the fluid variables have to be recovered from the conformally transformed matter sources. This problem has been addressed, although in a different context, by Dain and Nagy (2002) [11]. We show that if the matter variables are restricted to a certain region, then the Einstein constraint equations have a unique solution in the weighted Sobolev spaces of fractional order. The regularity depends upon the fractional power of the equation of state.
PB Academic Press Inc Elsevier Science
SN 0022-0396
YR 2011
FD 2011-09-15
LK https://hdl.handle.net/20.500.14352/42028
UL https://hdl.handle.net/20.500.14352/42028
LA eng
NO MICINN
NO UCM-BSCH
NO ORT Braude College's Research Authority
DS Docta Complutense
RD 8 abr 2025