The global nonlinear stability of the Minkowski space

D. Christodoulou; S. Klainerman

Séminaire Équations aux dérivées partielles (Polytechnique) (1989-1990)

  • page 1-29

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Christodoulou, D., and Klainerman, S.. "The global nonlinear stability of the Minkowski space." Séminaire Équations aux dérivées partielles (Polytechnique) (1989-1990): 1-29. <http://eudml.org/doc/111984>.

@article{Christodoulou1989-1990,
author = {Christodoulou, D., Klainerman, S.},
journal = {Séminaire Équations aux dérivées partielles (Polytechnique)},
keywords = {nonlinear gravitational stability; Minkowski space-time; geodesically complete; Einstein-Vacuum equation; asymptotically flat},
language = {eng},
pages = {1-29},
publisher = {Ecole Polytechnique, Centre de Mathématiques},
title = {The global nonlinear stability of the Minkowski space},
url = {http://eudml.org/doc/111984},
year = {1989-1990},
}

TY - JOUR
AU - Christodoulou, D.
AU - Klainerman, S.
TI - The global nonlinear stability of the Minkowski space
JO - Séminaire Équations aux dérivées partielles (Polytechnique)
PY - 1989-1990
PB - Ecole Polytechnique, Centre de Mathématiques
SP - 1
EP - 29
LA - eng
KW - nonlinear gravitational stability; Minkowski space-time; geodesically complete; Einstein-Vacuum equation; asymptotically flat
UR - http://eudml.org/doc/111984
ER -

References

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  1. [Ba1] R. Bartnik.Existence of maximal surfaces in asympt. flat Space-Times. Comm. Math. Phys.94, 1984, 155-175. Zbl0548.53054MR761792
  2. [Ba2] R. Bartnik.The mass of an Asymptotically flat manifold. Comm. Pure. Appl. Math.39, 1986, 661-693. Zbl0598.53045MR849427
  3. [Bo] H. Bondi..Nature186, 1960, 535. Zbl0087.42504
  4. [Bo-Bu-Me] H. Bondi - M.G.J. van der Burg- A.W.K. Metzner.Gravitational waves in General Relativity vii. Proc. Roy. Soc. Lond.A269, 1962, 21-52. Zbl0106.41903
  5. [Br] C. Bruhat.Theoreme d' existence pour certain systemes d'equations aux dérivées partielles nonlinaires. Acta Matematica88 (1952), 141-225. Zbl0049.19201MR53338
  6. [Ch] D. Christodoulou.Global solutions for nonlinear hyperbolic equations for small data. Comm. Pure appl. Math.39, 1986, 267-282. Zbl0612.35090MR820070
  7. [Ch-Br] C. Bruhat- D. Christodoulou.Elliptic systems in Hs,δ spaces on manifolds which are Euclidean at infinity. Acta Math.145, 1981,129-150. Zbl0484.58028
  8. [Ch-Eb] J. Cheeger - D. Ebin.Comparison theorems in Riemannian Geometry. North -Holland Publ. Comp.1975. Zbl0309.53035MR458335
  9. [Ch-K1] D. Christodoulou- S. Klainerman.Asymptotic properties of linear field equations in Minkowski space. preprint. Zbl0715.35076MR1038141
  10. [Ch-Mu] D. Christodoulou-N.O' Murchadha. The boost problem in General Relativity. Comm. Math. Phys.80, 1981, 271-300. Zbl0477.35081MR623161
  11. [Eisen] L.P. Eisenhart.Riemannian Geometry. Princeton University Press1926. MR1487892JFM52.0721.01
  12. [Gi-Tr] D. Gilbarg- N.S. Trudinger.Ellptic partial differential equations of second order. Springer- Verlag1977. Zbl0361.35003MR473443
  13. [Ho] L. Hörmander.On Sobolev spaces associated with some Lie Algebras. Report NO:4, Inst. Mittag-Leffler1985. Zbl0658.46023MR1112150
  14. [John] F. John.Formation of Singularities in Elastic Waves. Lecture Notes in Phys. Springer-Verlag1984 pages 190-214. Zbl0563.73022MR755727
  15. [K11] S. Klainerman.The null condition and global existence to nonlinear wave equat ions. Lect. Appl. Math.23, 1986, 293-326. Zbl0599.35105MR837683
  16. [K12] S. Klainerman.Remarks on the global Sobolev inequalities in Minkowski Space. Comm. Pure appl. Math.40, 1987, 111-117. Zbl0686.46019MR865359
  17. [K13] S. Klainerman.Unform decay estimates and the Lorentz invariance of the classical wave equation. Comm. Pure appl. Math.38,1985, 321-332. Zbl0635.35059MR784477
  18. [Ne-To] E.T. Newman- K.P. Todd.Asymptotically flat space-times. Genral Relativity and Gravitation, vol 2, A. Held, Plenum1980. MR617917
  19. [Oss] R. Osserman.The isoperimetric Inequality. Bull A.M.S.84, Nov. 1978,1182-1238. Zbl0411.52006MR500557
  20. [Pe1] R. Penrose.Structure of Space-Time. Batelle Rencontre, C.M.De Witt and J.A. Wheeler 1967. Zbl0174.55901
  21. [Pe2] R. Penrose.Zero rest mass fields including gravitation: Asymptotic behaviour. Proc. Roy. Soc. Lond.A284, 1962, 159-203. Zbl0129.41202MR175590
  22. [Sa] R.K. Sacks.Gravitational waves in General Relativity viii. Proc. Roy. Soc. Lond.A270, 1962, 103-126. Zbl0101.43605MR149908
  23. [Si] T. Sideris.Formation of Singularities in 3-d Compressible Fluids. Comm. Math. Phys.101, 1985, 475-485. Zbl0606.76088MR815196

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