Inégalités de Sogge bilinéaires et équation de Schrödinger non linéaire
Séminaire Équations aux dérivées partielles (Polytechnique) (2002-2003), Talk no. 17, 22 p.
@article{SEDP_2002-2003____A17_0,
     author = {Burq, Nicolas and G\'erard, Patrick and Tzvetkov, Nikolay},
     title = {In\'egalit\'es de Sogge bilin\'eaires et \'equation de Schr\"odinger non lin\'eaire},
     journal = {S\'eminaire \'Equations aux d\'eriv\'ees partielles (Polytechnique)},
     publisher = {Centre de math\'ematiques Laurent Schwartz, \'Ecole polytechnique},
     year = {2002-2003},
     note = {talk:17},
     mrnumber = {2030712},
     language = {fr},
     url = {http://www.numdam.org/item/SEDP_2002-2003____A17_0}
}
Burq, Nicolas; Gérard, Patrick; Tzvetkov, Nikolay. Inégalités de Sogge bilinéaires et équation de Schrödinger non linéaire. Séminaire Équations aux dérivées partielles (Polytechnique) (2002-2003), Talk no. 17, 22 p. http://www.numdam.org/item/SEDP_2002-2003____A17_0/

[1] V. Banica. Thèse, Université de Paris–Sud, en préparation.

[2] A. Besse. Manifolds all of whose geodesics are closed. Springer-Verlag, 1978. Berlin-New York. | MR 496885 | Zbl 0387.53010

[3] J. Bourgain. Fourier transform restriction phenomena for certain lattice subsets and application to nonlinear evolution equations I. Schrödinger equations. Geom. and Funct. Anal., 3 : 107–156, 1993. | MR 1209299 | Zbl 0787.35097

[4] J. Bourgain. Exponential sums and nonlinear Schrödinger equations. Geom. and Funct. Anal., 3 :157–178, 1993. | MR 1209300 | Zbl 0787.35096

[5] J.  Bourgain. Refinements of Strichartz’ inequality and applications to 2D-NLS with critical nonlinearity IMRN, 253-283, 1998. | Zbl 0917.35126

[6] J. Bourgain. Global solutions of nonlinear Schrödinger equations. Colloq. Publications, American Math. Soc., 1999. | MR 1691575 | Zbl 0933.35178

[7] H. Brézis, T. Gallouët. Nonlinear Schrödinger evolution equations. Nonlinear Analysis, Theory, Methods and Applications, 4 :677–681, 1980. | MR 582536 | Zbl 0451.35023

[8] N. Burq, P. Gérard, N. Tzvetkov. Strichartz inequalities and the nonlinear Schrödinger equation on compact manifolds. Amer. J. Math. (à paraître). | MR 2058384 | Zbl 1067.58027

[9] N. Burq, P. Gérard, N. Tzvetkov. An instability property of the nonlinear Schrödinger equation on S d . Math. Res. Lett., 9 : 323-335, 2002. | MR 1909648 | Zbl 1003.35113

[10] N. Burq, P. Gérard, N. Tzvetkov. Two singular dynamics of the nonlinear Schrödinger equation on a plane domain, Preprint 2002, Geom. and Funct. Anal. (à paraître). | MR 1978490 | Zbl 1044.35084

[11] N. Burq, P. Gérard, N. Tzvetkov. An example of singular dynamics for the nonlinear Schrödinger equation on bounded domains. in Proceedings of the conference on Hyperbolic PDEs and related topics, Cortona, September 2002, F. Colombini–T. Nishitani editors, à paraître. | MR 2056842 | Zbl 02072521

[12] N. Burq, P. Gérard, N. Tzvetkov. The Cauchy problem for the nonlinear Schrödinger equation on compact manifold. J. Nonlinear Math. Physics, 2002 (à paraître). | MR 2063542

[13] L. Carleson, P. Sjölin. Oscillatory integrals and a multiplier problem for the disc. Studia Math., 44 : 287-299, 1972. | MR 361607 | Zbl 0215.18303

[14] T. Cazenave, F. Weissler. The Cauchy problem for the critical nonlinear Schrödinger equation in H s . Nonlinear Analysis, Theory, Methods and Applications, 807–836, 1990. | MR 1055532 | Zbl 0706.35127

[15] Y. Colin de Verdière. Le spectre des opérateurs elliptiques à bicaractéristiques toutes périodiques. Comment. Math. Helvetici, 54 :508–522, 1979. | MR 543346 | Zbl 0459.58014

[16] J. Ginibre. Le problème de Cauchy pour des EDP semi-linéaires périodiques en variables d’espace (d’après Bourgain). Séminaire Bourbaki 796, Astérique. 237 : 163-187, 1995. | Numdam | Zbl 0870.35096

[17] J. Ginibre, G. Velo. Smoothing properties and retarded estimates for some dispersive evolution equations. Commun. Math. Phys., 144 :163–188, 1992. | MR 1151250 | Zbl 0762.35008

[18] V. Guillemin. Lectures on spectral theory of elliptic operators. Duke Math. J., 44 :129–137, 1977. | MR 448452 | Zbl 0447.58033

[19] L. Hörmander. The spectral function of an elliptic operator. Acta Math., 121 :193–218, 1968. | MR 609014 | Zbl 0164.13201

[20] L. Hörmander. Oscillatory integrals and multipliers on FL p , Ark. Mat., 11 : 1-11, 1973. | MR 340924 | Zbl 0254.42010

[21] T. Kato. On nonlinear Schrödinger equations. Ann. I.H.P. (Phys. Théor.), 46 :113–129, 1987. | Numdam | MR 877998 | Zbl 0632.35038

[22] S. Klainerman, M. Machedon (with appendices by J. Bourgain and D. Tataru) Remark on Strichartz-type inequalities IMRN 201-220, 1996. | MR 1383755 | Zbl 0853.35062

[23] D. Robert. Autour de l’approximation semi-classique, volume 68 of Progress in Mathematics. Birkhaüser, 1987. | Zbl 0621.35001

[24] C. Sogge. Oscillatory integrals and spherical harmonics. Duke Math. Jour., 53 : 43–65, 1986. | MR 835795 | Zbl 0636.42018

[25] C. Sogge. Concerning the L p norm of spectral clusters for second order elliptic operators on compact manifolds. Jour. of Funct. Anal., 77 :123–138, 1988. | MR 930395 | Zbl 0641.46011

[26] C. Sogge. Fourier integrals in classical analysis. Cambridge tracts in Mathematics, 1993. | MR 1205579 | Zbl 0783.35001

[27] R. Stanton, A. Weinstein On the L 4 norm of spherical harmonics. Math. Proc. Camb. Phil. Soc., 89 :343-358, 1981. | MR 600249 | Zbl 0479.33010

[28] T. Tao. Multilinear weighted convolutions of L 2 functions, and applications to non-linear dispersive equations. Amer. J. Math. 123 : 839-908, 2001. | MR 1854113 | Zbl 0998.42005