Global existence for the einstein vacuum equations in wave coordinates

Communications in Mathematical Physics

Volumn 256, Issue 1, 2005, Pages 43-110

  Lindblad, Hans ^a   Rodnianski, Igor ^b  

^a UNIVERSITY OF CALIFORNIA   (United States)

^b PRINCETON UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 17444370107     PISSN: 00103616     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00220-004-1281-6     Document Type: Article

References (32)

1. [A1] Alinhac, S.: Rank 2 singular solutions for quasilinear wave equations. Int. Math. Res. Notices (18), 955-984 (2000)
2. [A2] Alinhac, S.: The null condition for quasilinear wave equations in two dimensions I. Invent. Math. 145, 597-618 (2001)
3. [A3] Alinhac, S.: An example of blowup at infinity for a quasilinear wave equation. Asterisque 284, 1-91 (2003)
4. [CB1] Choquet-Bruhat, Y.: Theoreme d'existence pour certains systemes d'equations aux derivees partielles nonlineaires. Acta Math. 88, 141-225 (1952)
5. [CB2] Choquet-Bruhat, Y.: Un theoreme d'instabilite pour certaines equations hyperboliques non line-aires. C. R. Acad. Sci. Paris Sr. A-B 276, A281-A284 (1973)
6. [CB3] Choquet-Bruhat, Y.: The null condition and asymptotic expansions for the Einstein's equations. Ann. Phys. (Leipzig) 9, 258-266 (2000)
7. [CB-G] Choquet-Bruhat, Y., Geroch, R.P.: Global aspects of the Cauchy problem in General Relativity. Commun. Math. Phys. 14, 329-335 (1969)
8. [C1] Christodoulou, D.: Global solutions of nonlinear hyperbolic equations for small initial data. Commun. Pure Appl. Math. 39, 267-282 (1986)
9. [C2] Christodoulou, D.: The Global Initial Value Problem in General Relativity. In: The Ninth Marcel Grossmann Meeting (Rome 2000), V.G. Gurzadyan, R.T. Jansen, (eds.), R. Ruffini, editor and series editor, River Edge, NJ: World Scientific, 2002, pp. 44-54
10. [C-K] Christodoulou, D., Klainerman, S.: The Global Nonlinear Stability of the Minkowski Space. Princeton Mathematical Series 41. Princeton, NJ: Princeton University Press, 1993
11. [C-D] Chruściel, P. T., Delay, E.: Existence of non-trivial, vacuum, asymptotically simple spacetimes. Class, Quantum Grav. 19(9), L71-L79 (2002)
12. [Co] Corvino, J.: Scalar curvature deformation and a gluing construction for the Einstein constraint equations. Commun. Math. Phys. 214(1), 137-189 (2000)
13. [Fo] Fock, V.: The theory of space, time and gravitation. New York: The Macmillan Co., 1964
14. [Fr] Friedrich, H.: On the existence of n-geodesically complete or future complete solutions of Einstein's field equations with smooth asymptotic structure. Commun. Math. Phys. 107(4), 587-609 (1986)
15. [H-E] Hawking, S., Ellis, G.: The large scale structure of space-time. Cambridge: Cambridge University Press, 1973
16. [H1] Hörmander, L.: The lifespan of classical solutions of nonlinear hyperbolic equations. In: Pseudo-differential operators (Oberwolfach, 1986), Lecture Notes in Math. 1256, Berlin: Springer, 1987, pp. 214-280
17. [H2] Hörmander, L.: Lectures on Nonlinear hyperbolic differential equations. Berlin-Heidelberg-New York: Springer Verlag, 1997
18. [H3] Hörmander, L.: On the fully nonlinear Cauchy probelm with small initial data II. In: Microlocal analysis and nonlinear waves (Minneapolis, MN, 1988-1989), IMA Vol. Math. Appl. 30, New York: Springer, 1991, pp. 51-81
19. [J1] John, P.: Blow-up for quasilinear wave equations in three space dimensions. Commun. Pure Appl. Math. 34(1), 29-51 (1981)
20. t) Δu in three space dimensions. Mat. Appl. Comput. 4(1), 3-18 (1985)
21. [J-K] John, F., Klainerman, S.: Almost global existence to nonlinear wave equations in three space dimensions. Commun. Pure Appl. Math. 37, 443-455 (1984)
22. [K1] Klainerman, S.: Uniform decay estimates and the Lorentz invariance of the wave equation. Commun. Pure Appl. Math. 38, 321-332 (1985)
23. [K2] Klainerman, S.: The null condition and global existence to nonlinear wave equations. Lect. Appl. Math. 23, 293-326 (1986)
24. [K-N1] Klainerman, S., Nicolo, P.: The evolution problem in general relativity. Basel-Boston: Birkhäuser, 2003
25. [K-N2] Klainerman, S., Nicolo, P.: Peeling properties of asymptotically flat solutions to the Einstein vacuum equations. Class. Quant. Grav. 20, 3215-3257 (2003)
26. [L1] Lindblad, H.: On the lifespan of solutions of nonlinear wave equations with small initial data. Commun. Pure Appl. Math 43, 445-472 (1990)
27. [L2] Lindblad, H.: Global solutions of nonlinear wave equations. Commun. Pure Appl. Math. 45(9), 1063-1096 (1992)
28. [L-R] Lindblad, H., Rodnianski, I.: The weak null condition for Einstein's equations. C. R. Math. Acad. Sci. Paris 336(11), 901-906 (2003)
29. [S1] Shu, W-T.: Asymptotic properties of the solutions of linear and nonlinear spin field equations in Minkowski space. Commun. Math. Phys 140(3), 449-480 (1991)
30. [S-Y] Schoen, R., Yau, S.: On the proof of the positive mass conjecture in general relativity. Commun. Math. Phys. 65, 45-76 (1979)
31. [Wa] Wald, R.: General Relativity. Chicago, IL: Chicago Univ. Press, 1984
32. [Wi] Witten, E.: A new proof of the positive mass theorem. Commun. Math. Phys. 80, 381-402 (1981)