@article{SEDP_2002-2003____A9_0, author = {Carles, R\'emi and Fermanian{\textendash}Kammerer, Clotilde and Gallagher, Isabelle}, title = {R\^ole des oscillations quadratiques dans des \'equations de {Schr\"odinger} non lin\'eaire}, journal = {S\'eminaire \'Equations aux d\'eriv\'ees partielles (Polytechnique) dit aussi "S\'eminaire Goulaouic-Schwartz"}, note = {talk:9}, pages = {1--12}, publisher = {Centre de math\'ematiques Laurent Schwartz, \'Ecole polytechnique}, year = {2002-2003}, zbl = {1064.35178}, language = {en}, url = {http://www.numdam.org/item/SEDP_2002-2003____A9_0/} }
TY - JOUR AU - Carles, Rémi AU - Fermanian–Kammerer, Clotilde AU - Gallagher, Isabelle TI - Rôle des oscillations quadratiques dans des équations de Schrödinger non linéaire JO - Séminaire Équations aux dérivées partielles (Polytechnique) dit aussi "Séminaire Goulaouic-Schwartz" N1 - talk:9 PY - 2002-2003 SP - 1 EP - 12 PB - Centre de mathématiques Laurent Schwartz, École polytechnique UR - http://www.numdam.org/item/SEDP_2002-2003____A9_0/ LA - en ID - SEDP_2002-2003____A9_0 ER -
%0 Journal Article %A Carles, Rémi %A Fermanian–Kammerer, Clotilde %A Gallagher, Isabelle %T Rôle des oscillations quadratiques dans des équations de Schrödinger non linéaire %J Séminaire Équations aux dérivées partielles (Polytechnique) dit aussi "Séminaire Goulaouic-Schwartz" %Z talk:9 %D 2002-2003 %P 1-12 %I Centre de mathématiques Laurent Schwartz, École polytechnique %U http://www.numdam.org/item/SEDP_2002-2003____A9_0/ %G en %F SEDP_2002-2003____A9_0
Carles, Rémi; Fermanian–Kammerer, Clotilde; Gallagher, Isabelle. Rôle des oscillations quadratiques dans des équations de Schrödinger non linéaire. Séminaire Équations aux dérivées partielles (Polytechnique) dit aussi "Séminaire Goulaouic-Schwartz" (2002-2003), Exposé no. 9, 12 p. http://www.numdam.org/item/SEDP_2002-2003____A9_0/
[1] H. Bahouri et P. Gérard: High frequency approximation of solutions to critical nonlinear wave equations, American Journal of Mathematics, 121, pages 131–175, 1999. | MR | Zbl
[2] H. Bahouri et P. Gérard: Concentration effects in critical nonlinear wave equations and scattering theory, Geometrical Optics and Related Topics (F. Colombini and N. Lerner eds), Progress in Nonlinear Differential Equation and Applications, vol. 32, Birkhäuser, Boston, 17–30, 1997. | MR | Zbl
[3] R. Carles: Geometric optics with caustic crossing for some nonlinear Schrödinger equations, Indiana Univ. Math. J. 49, pages 475–551, 2000. | MR | Zbl
[4] R. Carles, C. Fermanian et I. Gallagher: On the role of quadratic oscillations in nonlinear Schrödinger equations, . | MR
[5] T. Cazenave: An introduction to nonlinear Schrödinger equations, Text. Met. Mat., vol. 26, Univ. Fed. Rio de Jan., 1993.
[6] T. Cazenave et F. Weissler: Rapidly decaying solutions of the nonlinear Schrödinger equation, Comm. Math. Phys., 147, 75–100, 1992. | MR | Zbl
[7] J. Duistermaat: Oscillatory integrals, Lagrange immersions and unfolding of singularities, Comm. Pure Appl. Math., 27, pages 207–281, 1974. | MR | Zbl
[8] I. Gallagher: Profile decomposition for the Navier–Stokes equations, Bulletin de la Société Mathématique de France, 129, pages 285–316, 2001. | Numdam | MR | Zbl
[9] P. Gérard: Oscillations and concentration effects in semilinear dispersive wave equations, J. Funct. Anal. 141, pages 60–98, 1996. | MR | Zbl
[10] P. Gérard: Description du défaut de compacité de l’injection de Sobolev, ESAIM Contrôle Optimal et Calcul des Variations, 3, pages 213–233, 1998 (version électronique: http://www.emath.fr/cocv/).
[11] J.-L. Joly, G. Metivier et J. Rauch: Caustics for dissipative semilinear oscillations, Mem. Amer. Math. Soc. 144, 2000. | MR | Zbl
[12] S. Keraani: On the defect of compactness for the Strichartz estimates of the Schrödinger equations, J. Differential Equations, 175, no. 2, 353–392, 2001. | MR | Zbl
[13] F. Merle: Determination of blow-up solutions with minimal mass for nonlinear Schrödinger equations with critical power, Duke Math. J., 69, no. 2, 427–454, 1993. | MR | Zbl
[14] F. Merle et L. Vega: Compactness at blow-up time for solutions of the critical nonlinear Schrödinger equation in 2D, Internat. Math. Res. Notices, no. 8, 399–425, 1998. | MR | Zbl
[15] J. Rauch: Partial Differential Equations, Graduate Texts in Math., vol. 128, Springer-Verlag, New York, 1991. | MR | Zbl