Inégalités de Sogge bilinéaires et équation de Schrödinger non linéaire

 Access to full text

 Full (PDF)

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. Zbl0387.53010MR496885
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. Zbl0787.35097MR1209299
4. J. Bourgain. Exponential sums and nonlinear Schrödinger equations. Geom. and Funct. Anal., 3 :157–178, 1993. Zbl0787.35096MR1209300
5. J.  Bourgain. Refinements of Strichartz’ inequality and applications to 2D-NLS with critical nonlinearity IMRN, 253-283, 1998. Zbl0917.35126
6. J. Bourgain. Global solutions of nonlinear Schrödinger equations. Colloq. Publications, American Math. Soc., 1999. Zbl0933.35178MR1691575
7. H. Brézis, T. Gallouët. Nonlinear Schrödinger evolution equations. Nonlinear Analysis, Theory, Methods and Applications, 4 :677–681, 1980. Zbl0451.35023MR582536
8. N. Burq, P. Gérard, N. Tzvetkov. Strichartz inequalities and the nonlinear Schrödinger equation on compact manifolds. Amer. J. Math. (à paraître). Zbl1067.58027MR2058384
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. Zbl1003.35113MR1909648
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). Zbl1044.35084MR1978490
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. Zbl1210.35225MR2056842
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). Zbl1003.35113MR2063542
13. L. Carleson, P. Sjölin. Oscillatory integrals and a multiplier problem for the disc. Studia Math., 44 : 287-299, 1972. Zbl0215.18303MR361607
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. Zbl0706.35127MR1055532
15. Y. Colin de Verdière. Le spectre des opérateurs elliptiques à bicaractéristiques toutes périodiques. Comment. Math. Helvetici, 54 :508–522, 1979. Zbl0459.58014MR543346
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. Zbl0870.35096
17. J. Ginibre, G. Velo. Smoothing properties and retarded estimates for some dispersive evolution equations. Commun. Math. Phys., 144 :163–188, 1992. Zbl0762.35008MR1151250
18. V. Guillemin. Lectures on spectral theory of elliptic operators. Duke Math. J., 44 :129–137, 1977. Zbl0447.58033MR448452
19. L. Hörmander. The spectral function of an elliptic operator. Acta Math., 121 :193–218, 1968. Zbl0164.13201MR609014
20. L. Hörmander. Oscillatory integrals and multipliers on $F{L}^p$, Ark. Mat., 11 : 1-11, 1973. Zbl0254.42010MR340924
21. T. Kato. On nonlinear Schrödinger equations. Ann. I.H.P. (Phys. Théor.), 46 :113–129, 1987. Zbl0632.35038MR877998
22. S. Klainerman, M. Machedon (with appendices by J. Bourgain and D. Tataru) Remark on Strichartz-type inequalities IMRN 201-220, 1996. Zbl0853.35062MR1383755
23. D. Robert. Autour de l’approximation semi-classique, volume 68 of Progress in Mathematics. Birkhaüser, 1987. Zbl0621.35001
24. C. Sogge. Oscillatory integrals and spherical harmonics. Duke Math. Jour., 53 : 43–65, 1986. Zbl0636.42018MR835795
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. Zbl0641.46011MR930395
26. C. Sogge. Fourier integrals in classical analysis. Cambridge tracts in Mathematics, 1993. Zbl0783.35001MR1205579
27. R. Stanton, A. Weinstein On the $L^4$ norm of spherical harmonics. Math. Proc. Camb. Phil. Soc., 89 :343-358, 1981. Zbl0479.33010MR600249
28. T. Tao. Multilinear weighted convolutions of $L^2$ functions, and applications to non-linear dispersive equations. Amer. J. Math. 123 : 839-908, 2001. Zbl0998.42005MR1854113