Bilinear space-time estimates for homogeneous wave equations

Annales Scientifiques de l'Ecole Normale Superieure

Volumn 33, Issue 2, 2000, Pages 211-274

  Foschi, Damiano ^a   Klainerman, Sergiu ^a  

^a PRINCETON UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0042229265     PISSN: 00129593     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0012-9593(00)00109-9     Document Type: Article

References (24)

1. Beals M., Bézard M. Low regularity local solutions for field equations. Comm. Partial Differential Equations. Vol. 21:(1-2):1996;79-124.
2. Foschi D. On a endpoint case of the Klainerman-Machedon estimates, Preprint. 1998.
3. Ginibre J., Velo G. Generalized Strichartz inequalities for the wave equation. J. Funct. Anal. Vol. 133:(1):1995;50-68.
4. Hörmander L. The Analysis of Linear Partial Differential Operators. I. 2nd ed. Springer Study Edition, Distribution Theory and Fourier Analysis. 1990;Springer, Berlin.
5. Keel M., Tao T. Endpoint Strichartz estimates. Amer. J. Math. Vol. 120:(5):1998;955-980.
6. Klainerman S., Machedon M. Space-time estimates for null forms and the local existence theorem. Comm. Pure Appl. Math. Vol. 46:(9):1993;1221-1268.
7. Klainerman S., Machedon M. On the Maxwell-Klein-Gordon equation with finite energy. Duke Math. J. Vol. 74:(1):1994;19-44.
8. 3+1 . Ann. of Math. Vol. 142:1995;39-119.
9. Klainerman S., Machedon M. Smoothing estimates for null forms and applications. Duke Math. J. Vol. 81:(1):1995;99-133. (A celebration of John F. Nash, Jr.).
10. s,δ . Int. Math. Res. Not. Vol. 17:1996;853-865.
11. Klainerman S., Machedon M. Remark on Strichartz-type inequalities. Int. Math. Res. Not. Vol. 5:1996;201-220.
12. Klainerman S., Machedon M. On the optimal regularity for gauge field theories. Differential and Integral Equations. Vol. 6:1997;1019-1030.
13. Klainerman S., Machedon M. On the regularity properties of a model problem related to wave maps. Duke Math. J. Vol. 87:(3):1997;553-589.
14. Klainerman S., Selberg S. Remark on the optimal regularity for equations of wave maps type. Comm. Partial Differential Equations. Vol. 22:(5-6):1997;901-918.
15. 4+1 , Preprint. 1998.
16. Selberg S. Multilinear space-time estimates and applications to local existence theory for nonlinear wave equations, Ph.D. Thesis. 1999;Princeton University.
17. Stein E.M. Harmonic Analysis: Real-Variable Methods, Orthogonality, and Oscillatory Integrals. 1993;Princeton University Press.
18. Strichartz R.S. Restrictions of Fourier transforms to quadratic surfaces and decay of solutions of wave equations. Duke Math. J. Vol. 44:(3):1977;705-714.
19. Tao T., private communication.
20. Tao T., Vargas A., Vega L. A bilinear approach to the restriction and Kakeya conjectures. J. Amer. Math. Soc. Vol. 11:(4):1998;967-1000.
21. Tataru D. On global existence and scattering for the wave maps equation, Preprint. 1998.
22. 2 in 5+1 dimensions, Preprint. 1999.
23. Tomas P.A. A restriction theorem for the Fourier transform. Bull. Amer. Math. Soc. Vol. 81:1975;477-478.
24. Wolff T. A sharp bilinear cone restriction estimate, Preprint. 1999.