Bilinear space-time estimates for homogeneous wave equations
Annales scientifiques de l'École Normale Supérieure, Serie 4, Volume 33 (2000) no. 2, p. 211-274
@article{ASENS_2000_4_33_2_211_0,
     author = {Foschi, Damiano and Klainerman, Sergi\`u},
     title = {Bilinear space-time estimates for homogeneous wave equations},
     journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure},
     publisher = {Elsevier},
     volume = {Ser. 4, 33},
     number = {2},
     year = {2000},
     pages = {211-274},
     doi = {10.1016/s0012-9593(00)00109-9},
     zbl = {0959.35107},
     mrnumber = {2001g:35145},
     language = {en},
     url = {http://www.numdam.org/item/ASENS_2000_4_33_2_211_0}
}
Foschi, Damiano; Klainerman, Sergiu. Bilinear space-time estimates for homogeneous wave equations. Annales scientifiques de l'École Normale Supérieure, Serie 4, Volume 33 (2000) no. 2, pp. 211-274. doi : 10.1016/s0012-9593(00)00109-9. http://www.numdam.org/item/ASENS_2000_4_33_2_211_0/

[1] Beals M., Bézard M., Low regularity local solutions for field equations, Comm. Partial Differential Equations 21 (1-2) (1996) 79-124. | MR 97e:35111 | Zbl 0852.35098

[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. 133 (1) (1995) 50-68. | MR 97a:46047 | Zbl 0849.35064

[4] Hörmander L., The Analysis of Linear Partial Differential Operators. I, 2nd ed., Springer Study Edition, Distribution Theory and Fourier Analysis, Springer, Berlin, 1990. | Zbl 0712.35001

[5] Keel M., Tao T., Endpoint Strichartz estimates, Amer. J. Math. 120 (5) (1998) 955-980. | MR 2000d:35018 | Zbl 0922.35028

[6] Klainerman S., Machedon M., Space-time estimates for null forms and the local existence theorem, Comm. Pure Appl. Math. 46 (9) (1993) 1221-1268. | MR 94h:35137 | Zbl 0803.35095

[7] Klainerman S., Machedon M., On the Maxwell-Klein-Gordon equation with finite energy, Duke Math. J. 74 (1) (1994) 19-44. | MR 95f:35210 | Zbl 0818.35123

[8] Klainerman S., Machedon M., Finite energy solutions of the Yang-Mills equations in ℝ3 + 1, Ann. of Math. 142 (1995) 39-119. | MR 96i:58167 | Zbl 0827.53056

[9] Klainerman S., Machedon M., Smoothing estimates for null forms and applications, Duke Math. J. 81 (1) (1995) 99-133 (A celebration of John F. Nash, Jr.). | MR 97h:35022 | Zbl 0909.35094

[10] Klainerman S., Machedon M., Estimates for null forms and the spaces Hs,δ, Int. Math. Res. Not. 17 (1996) 853-865. | MR 98j:46028 | Zbl 0909.35095

[11] Klainerman S., Machedon M., Remark on Strichartz-type inequalities, Int. Math. Res. Not. 5 (1996) 201-220. | MR 97g:46037 | Zbl 0853.35062

[12] Klainerman S., Machedon M., On the optimal regularity for gauge field theories, Differential and Integral Equations 6 (1997) 1019-1030. | MR 2000d:58043 | Zbl 0940.35011

[13] Klainerman S., Machedon M., On the regularity properties of a model problem related to wave maps, Duke Math. J. 87 (3) (1997) 553-589. | MR 98e:35118 | Zbl 0878.35075

[14] Klainerman S., Selberg S., Remark on the optimal regularity for equations of wave maps type, Comm. Partial Differential Equations 22 (5-6) (1997) 901-918. | MR 99c:35163 | Zbl 0884.35102

[15] Klainerman S., Tataru D., On the optimal regularity for Yang-Mills equations in ℝ4+1, Preprint, 1998.

[16] Selberg S., Multilinear space-time estimates and applications to local existence theory for nonlinear wave equations, Ph.D. Thesis, Princeton University, 1999.

[17] Stein E.M., Harmonic Analysis : Real-Variable Methods, Orthogonality, and Oscillatory Integrals, Princeton University Press, 1993. | MR 95c:42002 | Zbl 0821.42001

[18] Strichartz R.S., Restrictions of Fourier transforms to quadratic surfaces and decay of solutions of wave equations, Duke Math. J. 44 (3) (1977) 705-714. | MR 58 #23577 | Zbl 0372.35001

[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. 11 (4) (1998) 967-1000. | MR 99f:42026 | Zbl 0924.42008

[21] Tataru D., On global existence and scattering for the wave maps equation, Preprint, 1998.

[22] Tataru D., On the equation □u = |∇u|² in 5 + 1 dimensions, Preprint, 1999.

[23] Tomas P.A., A restriction theorem for the Fourier transform, Bull. Amer. Math. Soc. 81 (1975) 477-478. | MR 50 #10681 | Zbl 0298.42011

[24] Wolff T., A sharp bilinear cone restriction estimate, Preprint, 1999.