Nonlinear stability of self-gravitating irrotational Chaplygin fluids in a FLRW geometry

LeFloch, Philippe G.; Wei, Changhua

doi:10.1016/j.anihpc.2020.09.005

LeFloch, Philippe G.¹ ; Wei, Changhua ²

¹ a Laboratoire Jacques-Louis Lions and Centre National de la Recherche Scientifique, Sorbonne Université, 4 Place Jussieu, 75252 Paris, France
² b Department of Mathematics, Zhejiang Sci-Tech University, Hangzhou 310018, PR China

Annales de l'I.H.P. Analyse non linéaire, mai – juin 2021, Tome 38 (2021) no. 3, pp. 787-814.

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Résumé

We analyze the global nonlinear stability of FLRW (Friedmann-Lemaître-Robertson-Walker) spacetimes in the presence of an irrotational perfect fluid. We assume that the fluid is governed by the so-called (generalized) Chaplygin equation of state $p = - \frac{A^{2}}{ρ^{α}}$ relating the pressure to the mass-energy density, in which $A > 0$ and $α \in (0, 1]$ are constants. We express the Einstein equations in wave gauge as a system of coupled nonlinear wave equations and, after performing a conformal transformation, we analyze the global behavior of solutions toward the future. Under small perturbations, the $(3 + 1)$ -spacetime metric, the mass-energy density, and the velocity vector describing the geometry and fluid unknowns remain globally close to a reference FLRW solution. Our analysis provides also the precise asymptotic behavior of the perturbed solutions toward the future.

DOI : 10.1016/j.anihpc.2020.09.005

Mots-clés : Einstein-Euler equations, FLRW cosmology, Generalized Chaplygin gas, Conformal transformation, Wave gauge

Affiliations des auteurs :

LeFloch, Philippe G. ¹ ; Wei, Changhua ²

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     title = {Nonlinear stability of self-gravitating irrotational {Chaplygin} fluids in a {FLRW} geometry},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {787--814},
     publisher = {Elsevier},
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LeFloch, Philippe G.; Wei, Changhua. Nonlinear stability of self-gravitating irrotational Chaplygin fluids in a FLRW geometry. Annales de l'I.H.P. Analyse non linéaire, mai – juin 2021, Tome 38 (2021) no. 3, pp. 787-814. doi : 10.1016/j.anihpc.2020.09.005. http://www.numdam.org/articles/10.1016/j.anihpc.2020.09.005/

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