Cubic Quasilinear wave equation and bilinear estimates
Hajer Bahouri[1]; Jean-Yves Chemin[2]
- [1] Université de Tunis, Département de Mathématiques, 1060 Tunis, Tunisia
- [2] Université Pierre-et-Marie-Curie, Analyse numérique 4, place Jussieu, 75230 Paris Cedex 05, France
Séminaire Équations aux dérivées partielles (2000-2001)
- Volume: 2000-2001, page 1-15
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topBahouri, Hajer, and Chemin, Jean-Yves. "Cubic Quasilinear wave equation and bilinear estimates." Séminaire Équations aux dérivées partielles 2000-2001 (2000-2001): 1-15. <http://eudml.org/doc/11013>.
@article{Bahouri2000-2001,
affiliation = {Université de Tunis, Département de Mathématiques, 1060 Tunis, Tunisia; Université Pierre-et-Marie-Curie, Analyse numérique 4, place Jussieu, 75230 Paris Cedex 05, France},
author = {Bahouri, Hajer, Chemin, Jean-Yves},
journal = {Séminaire Équations aux dérivées partielles},
keywords = {Energy methods; local wellposedness},
language = {eng},
pages = {1-15},
publisher = {Centre de mathématiques Laurent Schwartz, École polytechnique},
title = {Cubic Quasilinear wave equation and bilinear estimates},
url = {http://eudml.org/doc/11013},
volume = {2000-2001},
year = {2000-2001},
}
TY - JOUR
AU - Bahouri, Hajer
AU - Chemin, Jean-Yves
TI - Cubic Quasilinear wave equation and bilinear estimates
JO - Séminaire Équations aux dérivées partielles
PY - 2000-2001
PB - Centre de mathématiques Laurent Schwartz, École polytechnique
VL - 2000-2001
SP - 1
EP - 15
LA - eng
KW - Energy methods; local wellposedness
UR - http://eudml.org/doc/11013
ER -
References
top- H. Bahouri and J.-Y. Chemin, Équations d’ondes quasilinéaires et inégalités de Strichartz, American Journal of Mathematics, 121, 1999, pages 1337–1377. Zbl0952.35073
- H. Bahouri and J.-Y. Chemin, Équations d’ondes quasilinéaires et effet dispersif, International Mathematical Research News, 21, 1999, pages 1141–1178. Zbl0938.35106
- H. Bahouri and J.-Y. Chemin, Microlocal analysis, bilinear estimates and cubic quasilinear wave equation, in preparation. Zbl1053.35098
- J.-M. Bony, Calcul symbolique et propagation des singularités pour les équations aux dérivées partielles non linéaires, Annales de l’École Normale Supérieure, 14, 1981, pages 209–246. Zbl0495.35024
- J.-M. Bony, personnal communication. Zbl0473.35021
- J.-M. Bony and J.-Y. Chemin, Espaces fonctionnels associés au calcul de Weyl-Hörmander, Bulletin de la Société Mathématique de France, 122, 1994, pages 77–118. Zbl0798.35172MR1259109
- J.-M. Bony and N. Lerner, Quantification asymptotique et microlocalisation d’ordre supérieur, Annales de l’École Normale Supérieure, 22, 1989, pages 377–433. Zbl0753.35005
- J.-Y. Chemin and C.-J. Xu, Inclusions de Sobolev en calcul de Weyl-Hörmander et systèmes sous-elliptiques, Annales de l’École Normale Supérieure, 30, 1997, pages 719–751. Zbl0892.35161
- J. Ginibre and G. Velo, Generalized Strichartz inequalities for the wave equation, Journal of Functional Analysis, 133, 1995, page 50–68. Zbl0849.35064MR1351643
- L. Hörmander, The analysis of linear partial differential equations, Springer Verlag, 1983. Zbl0521.35002
- L. Kapitanski, Some generalization of the Strichartz-Brenner inequality, Leningrad Mathematical Journal, 1, 1990, pages 693–721. Zbl0732.35118
- S. Klainerman, The null condition and global existence to non linear wave equations, Communications in Pure and Applied Mathematics, 38, 1985, pages 631–641. Zbl0597.35100
- S. Klainerman and M. Machedon, Space-time estimates for null forms and the local existence theorem, Communications in Pure and Applied Mathematics, 46, 1993, pages 1221–1268. Zbl0803.35095MR1231427
- S. Klainerman and M. Machedon, Smoothing estimates for null forms and applications, Duke Mathematical Journal, 81, 1995, pages 99–133. Zbl0909.35094MR1381973
- S. Klainerman and M. Machedon, On the regularity properties of a model problem relates to wave maps, Duke Mathematical Journal, 87, 1997, pages 553–589. Zbl0878.35075MR1446618
- S. Klainerman and M. Machedon, Estimates for null forms and the spaces , International Mathematical Research News, 15, 1998, pages 756–774. Zbl0919.46023
- S. Klainerman and D. Tataru, On the optimal local regularity for the Yang-Mills equations in , Journal of the American Mathematical Society, 12, 1999, pages 93–116. Zbl0924.58010MR1626261
- H. Lindblad, A sharp couternexample to local existence of low regularity solutions to non linear wave equations, Duke Mathematical Journal, 72, 1993, pages 503–539. Zbl0797.35123MR1248683
- G. Ponce and T. Sideris, Local regularity of non linear wave equations in three space dimensions, Communications in Partial Differential Equations, 18, 1993, pages 169–177. Zbl0803.35096MR1211729
- H. Smith, A parametrix construction for wave equation with coefficients, Annales de l’Institut Fourier, 48, 1998, pages 797–835. Zbl0974.35068
- D. Tataru, Local and global results for wave maps I, Communications in Partial Differential Equations, 23, 1998, pages 1781–1793. Zbl0914.35083MR1641721
- D. Tataru, Strichartz estimates for second order hyperbolic operators with nonsmooth coefficients III, preprint Zbl0990.35027MR1887639
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