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

How to cite

top

Bahouri, 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
  1. 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
  2. H. Bahouri and J.-Y. Chemin, Équations d’ondes quasilinéaires et effet dispersif, International Mathematical Research News, 21, 1999, pages 1141–1178. Zbl0938.35106
  3. H. Bahouri and J.-Y. Chemin, Microlocal analysis, bilinear estimates and cubic quasilinear wave equation, in preparation. Zbl1053.35098
  4. 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
  5. J.-M. Bony, personnal communication. Zbl0473.35021
  6. 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
  7. 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
  8. 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
  9. J. Ginibre and G. Velo, Generalized Strichartz inequalities for the wave equation, Journal of Functional Analysis, 133, 1995, page 50–68. Zbl0849.35064MR1351643
  10. L. Hörmander, The analysis of linear partial differential equations, Springer Verlag, 1983. Zbl0521.35002
  11. L. Kapitanski, Some generalization of the Strichartz-Brenner inequality, Leningrad Mathematical Journal, 1, 1990, pages 693–721. Zbl0732.35118
  12. 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
  13. 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
  14. S. Klainerman and M. Machedon, Smoothing estimates for null forms and applications, Duke Mathematical Journal, 81, 1995, pages 99–133. Zbl0909.35094MR1381973
  15. 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
  16. S. Klainerman and M. Machedon, Estimates for null forms and the spaces  H s , δ , International Mathematical Research News, 15, 1998, pages 756–774. Zbl0919.46023
  17. S. Klainerman and D. Tataru, On the optimal local regularity for the Yang-Mills equations in  R 4 + 1 , Journal of the American Mathematical Society, 12, 1999, pages 93–116. Zbl0924.58010MR1626261
  18. 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
  19. 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
  20. H. Smith, A parametrix construction for wave equation with  C 1 , 1 coefficients, Annales de l’Institut Fourier, 48, 1998, pages 797–835. Zbl0974.35068
  21. D. Tataru, Local and global results for wave maps I, Communications in Partial Differential Equations, 23, 1998, pages 1781–1793. Zbl0914.35083MR1641721
  22. D. Tataru, Strichartz estimates for second order hyperbolic operators with nonsmooth coefficients III, preprint Zbl0990.35027MR1887639

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.