Geodesic
The nonlinear future stability of the FLRW family of solutions to the irrotational Euler–Einstein system with a positive cosmological constant
Journal of the European Mathematical Society, Tome 15 (2013) no. 6, pp. 2369-2462.

Voir la notice de l'article provenant de la source EMS Press

In this article, we study small perturbations of the family of Friedmann-Lemaître-Robertson-Walker cosmological background solutions to the coupled Euler-Einstein system with a positive cosmological constant in 1+3 spacetime dimensions. The background solutions model an initially uniform quiet fluid of positive energy density evolving in a spacetime undergoing exponentially accelerated expansion. Our nonlinear analysis shows that under the equation of state p=c2ρ,01/3, the background metric + fluid solutions are globally future-stable under small irrotational perturbations of their initial data. In particular, we prove that the perturbed spacetime solutions, which have the topological structure [0,∞)XT3, are future causally geodesically complete. Our analysis is based on a combination of energy estimates and pointwise decay estimates for quasilinear wave equations featuring dissipative inhomogeneous terms. Our main new contribution is showing that when 01/3, exponential spacetime expansion is strong enough to suppress the formation of fluid shocks. This contrasts against a well-known result of Christodoulou, who showed that in Minkowski spacetime, the corresponding constant-state irrotational fluid solutions are unstable.
DOI : 10.4171/jems/424
Classification : 35-XX, 83-XX
Keywords: cosmological constant, energy dissipation, expanding spacetime, geodesically complete, global existence, irrotational fluid, relativistic fluid, wave coordinates 
@article{JEMS_2013_15_6_a13,
     author = {Igor Rodnianski and Jared Speck},
     title = {The nonlinear future stability of the {FLRW} family of solutions to the irrotational {Euler{\textendash}Einstein} system with a positive cosmological constant},
     journal = {Journal of the European Mathematical Society},
     pages = {2369--2462},
     publisher = {mathdoc},
     volume = {15},
     number = {6},
     year = {2013},
     doi = {10.4171/jems/424},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/jems/424/}
}
TY  - JOUR
AU  - Igor Rodnianski
AU  - Jared Speck
TI  - The nonlinear future stability of the FLRW family of solutions to the irrotational Euler–Einstein system with a positive cosmological constant
JO  - Journal of the European Mathematical Society
PY  - 2013
SP  - 2369
EP  - 2462
VL  - 15
IS  - 6
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.4171/jems/424/
DO  - 10.4171/jems/424
ID  - JEMS_2013_15_6_a13
ER  - 
%0 Journal Article
%A Igor Rodnianski
%A Jared Speck
%T The nonlinear future stability of the FLRW family of solutions to the irrotational Euler–Einstein system with a positive cosmological constant
%J Journal of the European Mathematical Society
%D 2013
%P 2369-2462
%V 15
%N 6
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.4171/jems/424/
%R 10.4171/jems/424
%F JEMS_2013_15_6_a13
Igor Rodnianski; Jared Speck. The nonlinear future stability of the FLRW family of solutions to the irrotational Euler–Einstein system with a positive cosmological constant. Journal of the European Mathematical Society, Tome 15 (2013) no. 6, pp. 2369-2462. doi : 10.4171/jems/424. http://geodesic.mathdoc.fr/articles/10.4171/jems/424/

Cité par Sources :