Skip to Main Content

Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

A remark on global existence for small initial data of the minimal surface equation in Minkowskian space time
HTML articles powered by AMS MathViewer

by Hans Lindblad PDF
Proc. Amer. Math. Soc. 132 (2004), 1095-1102 Request permission

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
  • Yvonne Choquet-Bruhat and Demetrios 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), no. 4, 481–506 (1982). MR 654209, DOI 10.24033/asens.1417
  • Demetrios Christodoulou, Global solutions of nonlinear hyperbolic equations for small initial data, Comm. Pure Appl. Math. 39 (1986), no. 2, 267–282. MR 820070, DOI 10.1002/cpa.3160390205
  • —, Oral communication, 1999.
  • Demetrios Christodoulou, Solutions globales des équations de Yang et Mills, C. R. Acad. Sci. Paris Sér. I Math. 293 (1981), no. 2, 139–141 (French, with English summary). MR 637111
  • D. Christodoulou and S. Klainerman, The nonlinear stability of Minkowski space-time, Princeton University Press, Princeton, NJ.
  • R. Hamilton, Oral Communication, Oberwolfach, 1994.
  • J. Hoppe, Some classical solutions of relativistic membrane equations in $4$-space-time dimensions, Phys. Lett. B 329 (1994), no. 1, 10–14. MR 1279146, DOI 10.1016/0370-2693(94)90510-X
  • Lars Hörmander, $L^1,\ L^\infty$ estimates for the wave operator, Analyse mathématique et applications, Gauthier-Villars, Montrouge, 1988, pp. 211–234. MR 956961
  • Lars Hörmander, Lectures on nonlinear hyperbolic differential equations, Mathématiques & Applications (Berlin) [Mathematics & Applications], vol. 26, Springer-Verlag, Berlin, 1997. MR 1466700
  • G. Huisken and M. Struwe, Oral communication, 1999.
  • F. John and S. Klainerman, Almost global existence to nonlinear wave equations in three space dimensions, Comm. Pure Appl. Math. 37 (1984), no. 4, 443–455. MR 745325, DOI 10.1002/cpa.3160370403
  • Sergiu Klainerman, Uniform decay estimates and the Lorentz invariance of the classical wave equation, Comm. Pure Appl. Math. 38 (1985), no. 3, 321–332. MR 784477, DOI 10.1002/cpa.3160380305
  • S. Klainerman, The null condition and global existence to nonlinear wave equations, Nonlinear systems of partial differential equations in applied mathematics, Part 1 (Santa Fe, N.M., 1984) Lectures in Appl. Math., vol. 23, Amer. Math. Soc., Providence, RI, 1986, pp. 293–326. MR 837683
  • Sergiu Klainerman, Global existence for nonlinear wave equations, Comm. Pure Appl. Math. 33 (1980), no. 1, 43–101. MR 544044, DOI 10.1002/cpa.3160330104
  • —, Long time behaviour of solutions to nonlinear wave equations, Proceedings of the International Congress of Mathematicians (Warsaw, 1983), PWN, Warsaw, 1984, pp. 1209–1215.
  • Ta Tsien Li and Yi Zhou, Life-span of classical solutions to nonlinear wave equations in two space dimensions, J. Math. Pures Appl. (9) 73 (1994), no. 3, 223–249. MR 1273703
  • Ta Tsien Li and Yi Zhou, Life-span of classical solutions to nonlinear wave equations in two-space-dimensions. II, J. Partial Differential Equations 6 (1993), no. 1, 17–38. MR 1210250
  • Hans Lindblad, On the lifespan of solutions of nonlinear wave equations with small initial data, Comm. Pure Appl. Math. 43 (1990), no. 4, 445–472. MR 1047332, DOI 10.1002/cpa.3160430403
  • Hans Lindblad, Global solutions of nonlinear wave equations, Comm. Pure Appl. Math. 45 (1992), no. 9, 1063–1096. MR 1177476, DOI 10.1002/cpa.3160450902
Similar Articles
  • Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 35-xx
  • Retrieve articles in all journals with MSC (2000): 35-xx
Additional Information
  • Hans Lindblad
  • Affiliation: Department of Mathematics, University of California at San Diego, La Jolla, California 92093-0112
  • Email: lindblad@math.ucsd.edu
  • Received by editor(s): December 9, 2002
  • Published electronically: September 18, 2003
  • Communicated by: David S. Tartakoff
  • © Copyright 2003 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 132 (2004), 1095-1102
  • MSC (2000): Primary 35-xx
  • DOI: https://doi.org/10.1090/S0002-9939-03-07246-0
  • MathSciNet review: 2045426