Counterexamples to local existence for nonlinear wave equations
Hans Lindblad (1994)
Journées équations aux dérivées partielles
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Hans Lindblad (1994)
Journées équations aux dérivées partielles
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S. Klainerman, Matei Machedon (1997)
Journées équations aux dérivées partielles
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Vladimir Georgiev, Pedro P. Schirmer (1995)
Mathematische Zeitschrift
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Vladimir Georgiev (1990)
Mathematische Zeitschrift
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Christopher D. Sogge (1993)
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J. M. Ghidaglia, R. Temam (1987)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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Igor Rodnianski (2005-2006)
Séminaire Bourbaki
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The paper provides a description of the wave map problem with a specific focus on the breakthrough work of T. Tao which showed that a wave map, a dynamic lorentzian analog of a harmonic map, from Minkowski space into a sphere with smooth initial data and a small critical Sobolev norm exists globally in time and remains smooth. When the dimension of the base Minkowski space is , the critical norm coincides with energy, the only manifestly conserved quantity in this (lagrangian) theory....
Sergiù Klainerman, Damiano Foschi (1999)
Journées équations aux dérivées partielles
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I will start with a short review of the classical restriction theorem for the sphere and Strichartz estimates for the wave equation. I then plan to give a detailed presentation of their recent generalizations in the form of “Bilinear Estimates”. In addition to the theory, which is now quite well developed, I plan to discuss a more general point of view concerning the theory. By investigating simple examples I will derive necessary conditions for such estimates to be true. I also...
Benaissa, Abbes, Messaoudi, Salim A. (2002)
Journal of Applied Mathematics
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