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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.
Albert Einstein, Kosmologische Betrachtungen zur allgemeinen Relativitätstheorie , Sitzungsberichte der Königlich Preußische Akademie der Wissenschaften (Berlin) 142-152
1917
Earlier work this paper cites.
Théophile de Donder, La gravifique Einsteinienne , Gauthier-Villars, Paris, 1921
1921
Earlier work this paper cites.
Yvonne Foures (Choquet)-Bruhat, Théorème d’existence pour certains systèmes d’équations aux dérivées partielles non linéaires , Acta Mathematica 88
1952
Earlier work this paper cites.
K. O. Friedrichs, Symmetric hyperbolic linear differential equations , Comm. Pure Appl. Math. 7
1954
Earlier work this paper cites.
L. Nirenberg, On elliptic partial differential equations , Ann. Scuola Norm. Sup. Pisa (3) 13
1959
Earlier work this paper cites.
R. Courant and D. Hilbert, Methods of mathematical physics. Vol. II , Wiley Classics Library, John Wiley & Sons Inc., New York, 1989, Partial differential equations, Reprint of the 1962 original, A Wiley-Interscience Publication. MR 1013360 (90k:35001)
1962
Earlier work this paper cites.
Roger Penrose, Gravitational collapse and space-time singularities , Phys. Rev. Lett. 14
1965
Earlier work this paper cites.
S. W. Hawking, The occurrence of singularities in cosmology. iii. causality and singularities , Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences 300
1967
Earlier work this paper cites.
Yvonne Choquet-Bruhat and Robert Geroch, Global aspects of the Cauchy problem in general relativity , Comm. Math. Phys. 14
1969
Earlier work this paper cites.
Richard Schoen and Shing Tung Yau, On the proof of the positive mass conjecture in general relativity , Comm. Math. Phys. 65
1979
Earlier work this paper cites.
Sergiu Klainerman and Andrew Majda, Singular limits of quasilinear hyperbolic systems with large parameters and the incompressible limit of compressible fluids , Comm. Pure Appl. Math. 34
1981
Earlier work this paper cites.
by same author, Proof of the positive mass theorem. II , Comm. Math. Phys. 79
1981
Earlier work this paper cites.
Edward Witten, A new proof of the positive energy theorem , Comm. Math. Phys. 80
1981
Earlier work this paper cites.
Barrett O’Neill, Semi-Riemannian geometry , Pure and Applied Mathematics, vol. 103, Academic Press Inc. [Harcourt Brace Jovanovich Publishers], New York, 1983, With applications to relativity. MR 719023 (85f:53002)
1983
Earlier work this paper cites.
A. Majda, Compressible fluid flow and systems of conservation laws in several space variables , Applied Mathematical Sciences, vol. 53, Springer-Verlag, New York, 1984. MR 748308 (85e:35077)
1984
Earlier work this paper cites.
Robert M. Wald, General relativity , University of Chicago Press, Chicago, IL, 1984. MR MR757180 (86a:83001)
1984
Cited alongside, same era.
Helmut Friedrich, On the existence of n n -geodesically complete or future complete solutions of Einstein’s field equations with smooth asymptotic structure , Comm. Math. Phys. 107
1986
Cited alongside, same era.
by same author, On the global existence and the asymptotic behavior of solutions to the Einstein-Maxwell-Yang-Mills equations , J. Differential Geom. 34
1991
Cited alongside, same era.
Demetrios Christodoulou and Sergiu Klainerman, The global nonlinear stability of the Minkowski space , Princeton Mathematical Series, vol. 41, Princeton University Press, Princeton, NJ, 1993. MR MR1316662 (95k:83006)
1993
Cited alongside, same era.
Uwe Brauer, Alan Rendall, and Oscar Reula, The cosmic no-hair theorem and the non-linear stability of homogeneous Newtonian cosmological models , Classical Quantum Gravity 11
Alan D. Rendall, Theorems on existence and global dynamics for the Einstein equations , Living Reviews in Relativity 8
2005
Later among the works it cites.
by same author, The Euler equations of compressible fluid flow , Bull. Amer. Math. Soc. (N.S.) 44
2007
Later among the works it cites.
by same author, The formation of shocks in 3-dimensional fluids , EMS Monographs in Mathematics, European Mathematical Society (EMS), Zürich, 2007. MR 2284927 (2008e:76104)
2007
Later among the works it cites.
by same author, Mathematical problems of general relativity. I , Zurich Lectures in Advanced Mathematics, European Mathematical Society (EMS), Zürich, 2008. MR MR2391586 (2008m:83008)
2008
Later among the works it cites.
Hans Ringström, Future stability of the Einstein-non-linear scalar field system , Invent. Math. 173
2008
Later among the works it cites.
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1994
Cited alongside, same era.
Michael E. Taylor, Partial differential equations. III , Applied Mathematical Sciences, vol. 117, Springer-Verlag, New York, 1997, Nonlinear equations, Corrected reprint of the 1996 original. MR MR1477408 (98k:35001)
1996
Cited alongside, same era.
Lars Hörmander, Lectures on nonlinear hyperbolic differential equations , Mathématiques & Applications (Berlin) [Mathematics & Applications], vol. 26, Springer-Verlag, Berlin, 1997. MR MR1466700 (98e:35103)
1997
Cited alongside, same era.
Jalal Shatah and Michael Struwe, Geometric wave equations , Courant Lecture Notes in Mathematics, vol. 2, New York University Courant Institute of Mathematical Sciences, New York, 1998. MR MR1674843 (2000i:35135)
1998
Cited alongside, same era.
Yan Guo and A. Shadi Tahvildar-Zadeh, Formation of singularities in relativistic fluid dynamics and in spherically symmetric plasma dynamics , Nonlinear partial differential equations (Evanston, IL, 1998), Contemp. Math., vol. 238, Amer. Math. Soc., Providence, RI, 1999, pp. 151–161. MR 1724661
1999
Cited alongside, same era.
Demetrios Christodoulou, The action principle and partial differential equations , Annals of Mathematics Studies, vol. 146, Princeton University Press, Princeton, NJ, 2000. MR 1739321 (2003a:58001)
2000
Cited alongside, same era.
Sean M. Carroll, The cosmological constant , Living Rev. Relativ. 4
2001
Cited alongside, same era.
Sergiu Klainerman and Francesco Nicolò, The evolution problem in general relativity , Progress in Mathematical Physics, vol. 25, Birkhäuser Boston Inc., Boston, MA, 2003. MR MR1946854 (2004f:58036)
2003
Cited alongside, same era.
Christopher D. Sogge, Lectures on non-linear wave equations , second ed., International Press, Boston, MA, 2008. MR 2455195 (2009i:35213)
2008
Later among the works it cites.
Lydia Bieri and Nina Zipser (eds.), Extensions of the stability theorem of the Minkowski space in general relativity , American Mathematical Society, Providence, RI, 2009
2009
Later among the works it cites.
Julien Loizelet, Solutions globales des équations d’Einstein-Maxwell , Ann. Fac. Sci. Toulouse Math. (6) 18
2009
Later among the works it cites.
2009
Later among the works it cites.
Jared Speck, The non-relativistic limit of the Euler-Nordström system with cosmological constant , Rev. Math. Phys. 21
2009
Later among the works it cites.
by same author, Well-posedness for the Euler-Nordström system with cosmological constant , J. Hyperbolic Differ. Equ. 6
2009
Later among the works it cites.
Piotr T. Chruściel, Gregory J. Galloway, and Daniel Pollack, Mathematical general relativity: a sampler , Bull. Amer. Math. Soc. (N.S.) 47
2010
Later among the works it cites.
Constantine M. Dafermos, Hyperbolic conservation laws in continuum physics , third ed., Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 325, Springer-Verlag, Berlin, 2010. MR 2574377
2010
Later among the works it cites.
Hans Lindblad and Igor Rodnianski, The global stability of Minkowski space-time in harmonic gauge , Annals of Mathematics 171
2010
Later among the works it cites.