Mathematics – Analysis of PDEs
Scientific paper
2011-02-08
Mathematics
Analysis of PDEs
Accepted for publication in Selecta Mathematica, 78 pages. arXiv admin note: significant text overlap with arXiv:0911.5501
Scientific paper
In this article, we study small perturbations of the family of Friedmann-Lema\^itre-Robertson-Walker cosmological background solutions to the 1 + 3 dimensional Euler-Einstein system with a positive cosmological constant. These background solutions describe an initially uniform quiet fluid of positive energy density evolving in a spacetime undergoing accelerated expansion. Our nonlinear analysis shows that under the equation of state pressure = c_s^2 * energy density, with 0 < c_s^2 < 1/3, the background solutions are globally future-stable. In particular, we prove that the perturbed spacetime solutions, which have the topological structure [0,infty) x T^3, are future causally geodesically complete. These results are extensions of previous results derived by the author in a collaboration with I. Rodnianski, in which the fluid was assumed to be irrotational. Our novel analysis of a fluid with non-zero vorticity is based on the use of suitably-defined energy currents.
No associations
LandOfFree
The Nonlinear Future-Stability of the FLRW Family of Solutions to the Euler-Einstein System with a Positive Cosmological Constant does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with The Nonlinear Future-Stability of the FLRW Family of Solutions to the Euler-Einstein System with a Positive Cosmological Constant, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The Nonlinear Future-Stability of the FLRW Family of Solutions to the Euler-Einstein System with a Positive Cosmological Constant will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-501937