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A remark on global existence for small initial data of the minimal surface equation in Minkowskian space time

Author(s): Hans Lindblad
Journal: Proc. Amer. Math. Soc. 132 (2004), 1095-1102.
MSC (2000): Primary 35-xx
Posted: September 18, 2003
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Abstract | References | Similar articles | Additional information

Abstract: We show that the nonlinear wave equation corresponding to the minimal surface equation in Minkowski space time has a global solution for sufficiently small initial data.


References:

[CC]
Y. Choquet-Bruhat and D. Christodoulou, Existence of global solutions of the Yang-Mills, Higgs and spinor field equations in $3+1$ dimensions, Ann. Sci. École Norm. Sup. (4) 14 (1981), 481-506. MR 84c:81041

[C1]
D. Christodoulou, Global solutions of nonlinear hyperbolic equations for small initial data, Comm. Pure Appl. Math. 39 (1986), 267-282. MR 87c:35111

[C2]
-, Oral communication, 1999.

[C3]
-, Solutions globales des équations de Yang et Mills, C. R. Acad. Sci. Paris (Series A) 293 (1981), 139-141. MR 82k:58089

[CK1]
D. Christodoulou and S. Klainerman, The nonlinear stability of Minkowski space-time, Princeton University Press, Princeton, NJ.

[Ha1]
R. Hamilton, Oral Communication, Oberwolfach, 1994.

[Ho1]
J. Hoppe, Some classical solutions of relativistic membrane equations in $4$-space-time dimensions., Phys. Lett. B 329, No. 1 (1994), 10-14. MR 95e:81180

[Hö1]
L. Hörmander, $L^{1}$, $L^{\infty }$ estimates for the wave operator, Analyse Mathématique et Applications, Gauthier-Villars, Paris, 1988, pp. 211-234. MR 90e:35113

[Hö2]
-, Lectures on nonlinear hyperbolic differential equations, Springer-Verlag, Berlin, 1997. MR 98e:35103

[HS1]
G. Huisken and M. Struwe, Oral communication, 1999.

[JK1]
F. John and S. Klainerman, Almost global existence to nonlinear wave equations in three space dimensions, Comm. Pure Appl. Math. 37 (1984), 443-455. MR 85k:35147

[K1]
S. Klainerman, Uniform decay estimates and the Lorentz invariance of the classical wave equation, Comm. Pure Appl. Math. 38 (1985), 321-332. MR 86i:35091

[K2]
-, The null condition and global existence to nonlinear wave equations, Lectures in Applied Mathematics, Vol. 23, Amer. Math. Soc., Providence, RI, pp. 293-326. MR 87h:35217

[K3]
-, Global existence for nonlinear wave equations, Comm. Pure Appl. Math. 33 (1980), 43-101. MR 81b:35050

[K4]
-, Long time behaviour of solutions to nonlinear wave equations, Proceedings of the International Congress of Mathematicians (Warsaw, 1983), PWN, Warsaw, 1984, pp. 1209-1215.

[LZ1]
T. Li and Y. Zhou, Life-span of classical solutions to nonlinear wave equations in two space dimensions, J. Math. Pures et Appl. 73(3) (1994), 223-249. MR 95c:35174

[LZ2]
T. Li and Y. Zhou, Life-span of classical solutions to fully nonlinear wave equations in two-space-dimensions II, J. Partial Differential Equations 6(1) (1993), 17-38. MR 95c:35175

[L1]
H. Lindblad, On the lifespan of solutions of nonlinear wave equations with small initial data, Comm. Pure Appl. Math. 43 (1990), 445-472. MR 91i:35129

[L2]
-, Global solutions of nonlinear wave equations, Comm. Pure Appl. Math. 45(9) (1992), 1063-1096. MR 94a:35080


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Additional Information:

Hans Lindblad
Affiliation: Department of Mathematics, University of California at San Diego, La Jolla, California 92093-0112
Email: lindblad@math.ucsd.edu

DOI: 10.1090/S0002-9939-03-07246-0
PII: S 0002-9939(03)07246-0
Received by editor(s): December 9, 2002
Posted: September 18, 2003
Communicated by: David S. Tartakoff
Copyright of article: Copyright 2003, American Mathematical Society


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