2011/02/08 by Speck, Jared · 4 citations
#35Q31 #35Q35 #35Q76 #83C05 #83F05 #Analysis of PDEs (math.AP) #Cosmology and Nongalactic Astrophysics (astro-ph.CO) #FOS: Mathematics #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn) #General Relativity and Quantum Cosmology (gr-qc) #Mathematical Physics (math-ph) #Primary: 35A01 #Secondary: 35L99
paper · doi:10.48550/arxiv.1102.1501
In this article, we study small perturbations of the family of Friedmann-Lemaître-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 = cs2 * energy density, with 0 < cs2 < 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 T3, 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.