Microlocal analysis, bilinear estimates and cubic quasilinear wave equation
Autour de l'analyse microlocale - Volume en l'honneur de Jean-Michel Bony, Astérisque, no. 284 (2003), 49 p. 
@incollection{AST_2003__284__93_0,
     author = {Bahouri, Hajer and Chemin, Jean-Yves},
     title = {Microlocal analysis, bilinear estimates and cubic quasilinear wave equation},
     booktitle = {Autour de l'analyse microlocale - Volume en l'honneur de Jean-Michel Bony},
     editor = {Lebeau Gilles},
     series = {Ast\'erisque},
     publisher = {Soci\'et\'e math\'ematique de France},
     number = {284},
     year = {2003},
     zbl = {1053.35098},
     mrnumber = {2003418},
     language = {en},
     url = {http://archive.numdam.org/item/AST_2003__284__93_0/}
}
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Bahouri, Hajer; Chemin, Jean-Yves. Microlocal analysis, bilinear estimates and cubic quasilinear wave equation, dans Autour de l'analyse microlocale - Volume en l'honneur de Jean-Michel Bony, Astérisque, no. 284 (2003), 49 p. http://archive.numdam.org/item/AST_2003__284__93_0/

[1] S. Alinhac - Blow up of small data solutions for a class of quasilinear wave équations in two space dimensions, Annals of Mathematics, 149, 1999, p. 97-127. | Article | EuDML 125548 | MR 1680539 | Zbl 1080.35043

[2] S. Alinhac, - Blow up of small data solutions for a class of quasilinear wave equations in two space dimensions II, Acta Mathematica, 182, 1999, p. 1-23. | Article | MR 1687180 | Zbl 0973.35135

[3] V. Arnold - Méthodes Mathématiques pour la Mécanique, Éditions Mir, Moscou, 1976. | Zbl 0385.70001

[4] H. Bahouri & J.-Y. Chemin - Équations d'ondes quasilinéaires et inégalités de Strichartz, American Journal of Mathematics, 121, 1999, p. 1337-1377. | Article | MR 1719798 | Zbl 0952.35073

[5] H. Bahouri & J.-Y. Chemin, - Équations d'ondes quasilinéaires et effet dispersif, International Mathematical Research News, 21, 1999, p. 1141-1178. | Article | MR 1728676 | Zbl 0938.35106

[6] 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, p. 209-246. | Article | EuDML 82073 | Numdam | MR 631751 | Zbl 0495.35024

[7] J.-M. Bony, - personnal communication.

[8] J.-M. Bony & J.-Y. Chemin - Espaces fonctionnels associés au calcul de Weyl-Hörmander, Bulletin de la Société Mathématique de France, 122, 1994, p. 77-118. | Article | EuDML 87683 | Numdam | MR 1259109 | Zbl 0798.35172

[9] J.-M. Bony & N. Lerner - Quantification asymptotique et microlocalisation d'ordre supérieur, Annales de l'École Normale Supérieure, 22, 1989, p. 377-433. | Article | EuDML 82256 | Numdam | MR 1011988 | Zbl 0753.35005

[10] J.-Y. Chemin & C.-J. Xu - Inclusions de Sobolev en calcul de Weyl-Hörmander et systèmes sous-elliptiques, Annales de l'École Normale Supérieure, 30, 1997, p. 719-751. | Article | EuDML 82448 | Numdam | MR 1476294 | Zbl 0892.35161

[11] L. Hörmander - The analysis of linear partial differential equations, Springer Verlag, 1983. | MR 2108588

[12] L. Hörmander, Lectures on Nonlinear Hyperbolic Differential Equations, Mathématiques et Applications, 26, Springer, 1996. | MR 1466700 | Zbl 0881.35001

[13] L. Kapitanski - Some generalization of the Strichartz-Brenner inequality, Leningrad Mathematical Journal, 1, 1990, p. 693-721. | MR 1015129 | Zbl 0732.35118

[14] S. Klainerman - Uniform decay estimates and the Lorentz invariance of the classical wave equation Communications in Pure and Applied Mathematics, 38, 1985, p. 321-332. | Article | MR 784477 | Zbl 0635.35059

[15] S. Klainerman, - The null condition and global existence to non linear wave equations, Communications in Pure and Applied Mathematics, 38, 1985, p. 631-641. | MR 803252 | Zbl 0597.35100

[16] S. Klainerman & M. Machedon - Space-time estimates for null forms and the local existence theorem, Communications in Pure and Applied Mathematics, 46, 1993, p. 1221-1268. | Article | MR 1231427 | Zbl 0803.35095

[17] S. Klainerman & M. Machedon, - Smoothing estimates for null forms and applications, Duke Mathematical Journal, 81, 1995, p. 99-133. | Article | MR 1381973 | Zbl 0909.35094

[18] S. Klainerman & M. Machedon, - On the regularity properties of a model problem related to wave maps, Duke Mathematical Journal, 87, 1997, p. 553-589. | MR 1446618 | Zbl 0878.35075

[19] S. Klainerman & M. Machedon, - Remark on Strichartz type inequalites (with an appendix of J. Bourgain and D. Tataru), International Mathematical Research News, 5, 1996, p. 201-220. | Article | MR 1383755 | Zbl 0853.35062

[20] S. Klainerman & M. Machedon, - Estimates for null forms and the spaces H s,δ , International Mathematical Research News, 15, 1998, p. 756-774. | Zbl 0919.46023

[21] S. Klainerman & T. Sideris - On almost global existence for nonrelativistic wave equations in 3D, Communications in Pure and Applied Mathematics, 49, 1996, p. 307-321. | Article | Zbl 0867.35064

[22] S. Klainerman & D. Tataru - On the optimal local regularity for the Yang-Mills equations in 𝐑 4+1 , Journal of the American Mathematical Society, 12, 1999, p. 93-116. | Article | Zbl 0924.58010

[23] H. Lindblad - A sharp counterexample to local existence of low regularity solutions to non linear wave equations, Duke Mathematical Journal, 72, 1993, p. 503-539. | Article | Zbl 0797.35123

[24] G. Ponce & T. Sideris - Local regularity of non linear wave equations in three space dimensions, Communications in Partial Differential Equations, 18, 1993, p. 169-177. | Article | Zbl 0803.35096

[25] H. Smith - A parametrix construction for wave equation with C 1,1 coefficients, Annales de l'Institut Fourier, 48, 1998, p. 797-835. | Article | EuDML 75304 | Numdam | Zbl 0974.35068

[26] E. M. Stein - Harnomic Analysis, Princeton University Press, 1993.

[27] D. Tataru - Strichartz estimates for operators with nonsmooth coefficients and the nonlinear wave equation, American Journal of Mathematics, 122, 2000, p. 349-376. | Article | Zbl 0959.35125

[28] D. Tataru, - Strichartz estimates for second order hyperbolic operators with nonsmooth coefficients II, American Journal of Mathematics, 123, 2001, p. 385-423. | Article | Zbl 0988.35037