@incollection{AST_2012__348__425_0, author = {Planchon, Fabrice}, title = {Existence globale et scattering pour les solutions de masse finie de l'\'equation de {Schr\"odinger} cubique en dimension deux [d'apr\`es {Benjamin} {Dodson,} {Rowan} {Killip,} {Terence} {Tao,} {Monica} {Vi\c{s}an} et {Xiaoyi} {Zhang]}}, booktitle = {S\'eminaire Bourbaki Volume 2010/2011 Expos\'es 1027-1042. Avec table par noms d'auteurs de 1948/49 \`a 2009/10.}, series = {Ast\'erisque}, note = {talk:1042}, pages = {425--447}, publisher = {Soci\'et\'e math\'ematique de France}, number = {348}, year = {2012}, mrnumber = {3051205}, zbl = {1296.35176}, language = {fr}, url = {http://archive.numdam.org/item/AST_2012__348__425_0/} }
TY - CHAP AU - Planchon, Fabrice TI - Existence globale et scattering pour les solutions de masse finie de l'équation de Schrödinger cubique en dimension deux [d'après Benjamin Dodson, Rowan Killip, Terence Tao, Monica Vişan et Xiaoyi Zhang] BT - Séminaire Bourbaki Volume 2010/2011 Exposés 1027-1042. Avec table par noms d'auteurs de 1948/49 à 2009/10. AU - Collectif T3 - Astérisque N1 - talk:1042 PY - 2012 SP - 425 EP - 447 IS - 348 PB - Société mathématique de France UR - http://archive.numdam.org/item/AST_2012__348__425_0/ LA - fr ID - AST_2012__348__425_0 ER -
%0 Book Section %A Planchon, Fabrice %T Existence globale et scattering pour les solutions de masse finie de l'équation de Schrödinger cubique en dimension deux [d'après Benjamin Dodson, Rowan Killip, Terence Tao, Monica Vişan et Xiaoyi Zhang] %B Séminaire Bourbaki Volume 2010/2011 Exposés 1027-1042. Avec table par noms d'auteurs de 1948/49 à 2009/10. %A Collectif %S Astérisque %Z talk:1042 %D 2012 %P 425-447 %N 348 %I Société mathématique de France %U http://archive.numdam.org/item/AST_2012__348__425_0/ %G fr %F AST_2012__348__425_0
Planchon, Fabrice. Existence globale et scattering pour les solutions de masse finie de l'équation de Schrödinger cubique en dimension deux [d'après Benjamin Dodson, Rowan Killip, Terence Tao, Monica Vişan et Xiaoyi Zhang], dans Séminaire Bourbaki Volume 2010/2011 Exposés 1027-1042. Avec table par noms d'auteurs de 1948/49 à 2009/10., Astérisque, no. 348 (2012), Exposé no. 1042, 23 p. http://archive.numdam.org/item/AST_2012__348__425_0/
[1] Optique géométrique généralisée pour les ondes non linéaires critiques, in Séminaire sur les Équations aux Dérivées Partielles, 1996-1997, École Polytech., 1997, p. exp. n° VIII, 17. | MR | Zbl
& -[2] High frequency approximation of solutions to critical nonlinear wave equations, Amer. J. Math. 121 (1999), p. 131-175. | DOI | MR | Zbl
& ,[3] Mass concentration phenomena for the -critical nonlinear Schrödinger equation, Trans. Amer. Math. Soc. 359 (2007), p. 5257-5282. | DOI | MR | Zbl
& -[4] Refinements of Strichartz' inequality and applications to 2D-NLS with critical nonlinearity, Int. Math. Res. Not. 1998 (1998), p. 253-283. | DOI | MR | Zbl
-[5] Global wellposedness of defocusing critical nonlinear Schrödinger equation in the radial case, J. Amer. Math. Soc. 12 (1999), p. 145-171. | DOI | MR | Zbl
,[6] Explosion pour l'équation de Schrödinger au régime du « log log » (d'apres Merle-Raphael), Séminaire Bourbaki, vol. 2005/2006, exp. n° 953, Astérisque 311 (2007), p. 33-53. | EuDML | Numdam | MR | Zbl
-[7] The Cauchy problem for the critical nonlinear Schrödinger equation in , Nonlinear Anal. 14 (1990), p. 807-836. | DOI | MR | Zbl
& -[8] Tensor products and correlation estimates with applications to nonlinear Schrödinger equations, Comm. Pure Appl. Math. 62 (2009), p. 920-968. | DOI | MR | Zbl
, & -[9] Global existence and scattering for rough solutions to generalized nonlinear Schrödinger equations on , Commun. Pure Appl. Anal. 7 (2008), p. 467-489. | DOI | MR | Zbl
, , & -[10] Almost conservation laws and global rough solutions to a nonlinear Schrödinger equation, Math. Res. Lett. 9 (2002), p. 659-682. | DOI | MR | Zbl
, , , & -[11] Global existence and scattering for rough solutions of a nonlinear Schrödinger equation on , Comm. Pure Appl. Math. 57 (2004), p. 987-1014. | DOI | MR | Zbl
, , , & ,[12] Global well-posedness and scattering for the energy-critical nonlinear Schrödinger equation in , Ann. of Math. 167 (2008), p. 767-865. | DOI | MR | Zbl
, , , & ,[13] Bootstrapped Morawetz estimates and resonant decomposition for low regularity global solutions of cubic NLS on , Commun. Pure Appl. Anal. 10 (2011), p. 397-414. | DOI | MR | Zbl
& -[14] Improved almost Morawetz estimates for the cubic nonlinear Schrödinger equation, Commun. Pure Appl. Anal. 10 (2011), p. 127-140. | DOI | MR | Zbl
-[15] Global well-posedness and scattering for the defocusing, -critical, nonlinear Schrödinger equation when , prépublication arXiv:1010.0040.
,[16] Global well-posedness and scattering for the defocusing, -critical, non-linear Schrödinger equation when , prépublication arXiv:1006.1375.
,[17] Global well-posedness and scattering for the defocusing, -critical, nonlinear Schrödinger equation when , prépublication arXiv:0912.2467.
,[18] Global well-posedness and scattering for the mass critical nonlinear schrödinger equation with mass below the mass of the ground state, prépublication arXiv:1104.1114. | DOI | MR
,[19] Conférence en l'honneur de L. Peletier, Université d'Orsay, 1998.
-[20] Le problème de Cauchy pour des EDP semi-linéaires périodiques en variables d'espace (d'après Bourgain), Séminaire Bourbaki, vol. 1994/95, exp. n° 796, Astérisque 237 (1996), p. 163-187. | EuDML | Numdam | MR | Zbl
-[21] Existence of solutions and scattering theory for the nonlinear Schrödinger equation, in Proceedings of the International Conference on Operator Algebras, Ideals, and their Applications in Theoretical Physics (Leipzig, 1977), Teubner, 1978, p. 320-334. | MR | Zbl
& -[22] Scattering theory in the energy space for a class of nonlinear Schrödinger equations, J. Math. Pures Appl. 64 (1985), p. 363-401. | MR | Zbl
& ,[23] Quadratic Morawetz inequalities and asymptotic completeness in the energy space for nonlinear Schrödinger and Hartree equations, Quart. Appl. Math. 68 (2010), p. 113-134. | DOI | MR | Zbl
& ,[24] A geometrical approach of existence of blow up solutions in for nonlinear Schrödinger equation, rapport n° R95031, Laboratoire d'Analyse Numérique, Univ. Pierre et Marie Curie, 1995.
& -[25] On the blowing up of solutions to the Cauchy problem for nonlinear Schrödinger equations, J. Math. Phys. 18 (1977), p. 1794-1797. | DOI | MR | Zbl
-[26] Endpoint Strichartz estimates, Amer. J. Math. 120 (1998), p. 955-980. | DOI | MR | Zbl
& -[27] Global well-posedness, scattering and blow-up for the energy-critical, focusing, non-linear Schrödinger equation in the radial case, Invent. Math. 166 (2006), p. 645-675. | DOI | MR | Zbl
& -[28] Global well-posedness, scattering and blow-up for the energy-critical focusing non-linear wave equation, Acta Math. 201 (2008), p. 147-212. | DOI | MR | Zbl
& ,[29] On the defect of compactness for the Strichartz estimates of the Schrödinger equations, J. Differential Equations 175 (2001), p. 353-392. | DOI | MR | Zbl
-[30] On the blow up phenomenon of the critical nonlinear Schrödinger equation, J. Funct. Anal. 235 (2006), p. 171-192. | DOI | MR | Zbl
,[31] The cubic nonlinear Schrödinger equation in two dimensions with radial data, J. Eur. Math. Soc. (JEMS) 11 (2009), p. 1203-1258. | DOI | MR | Zbl
, & -[32] Nonlinear Schrödinger equations at critical regularity, Clay Lecture Notes (2008). | MR
& -[33] The mass-critical nonlinear Schrödinger equation with radial data in dimensions three and higher, Anal. PDE 1 (2008), p. 229-266. | DOI | MR | Zbl
, & -[34] A priori bounds for the 1D cubic NLS in negative Sobolev spaces, Int. Math. Res. Not. 2007 (2007), Art. ID rnm053, 36. | DOI | MR | Zbl
& -[35] Decay and scattering of solutions of a nonlinear Schrödinger equation, J. Funct. Anal. 30 (1978), p. 245-263. | DOI | MR | Zbl
& -[36] Stability of blow-up profile and lower bounds for blow-up rate for the critical generalized KdV equation, Ann. of Math. 155 (2002), p. 235-280. | DOI | MR | Zbl
& -[37] On universality of blow-up profile for critical nonlinear Schrödinger equation, Invent. Math. 156 (2004), p. 565-672. | DOI | MR | Zbl
& -[38] Compactness at blow-up time for solutions of the critical nonlinear Schrödinger equation in 2D, Int. Math. Res. Not. 1998 (1998), p. 399-425. | DOI | MR | Zbl
& -[39] Restriction theorems and maximal operators related to oscillatory integrals in , Duke Math. J. 96 (1999), p. 547-574. | DOI | MR | Zbl
, & -[40] Bilinear virial identities and applications, Ann. Sci. Éc. Norm. Supér. 42 (2009), p. 261-290. | DOI | EuDML | Numdam | MR | Zbl
& -[41] Stability and blow up for the non linear Schrödinger equation, Clay Lecture Notes (2008).
-[42] Restrictions of Fourier transforms to quadratic surfaces and decay of solutions of wave equations, Duke Math. J. 44 (1977), p. 705-714. | DOI | MR | Zbl
-[43] The nonlinear Schrödinger equation, self-focusing and wave collapse, Applied Mathematical Sciences, vol. 139, Springer, 1999. | MR | Zbl
& -[44] Global well-posedness and scattering for the defocusing mass-critical nonlinear Schrödinger equation for radial data in high dimensions, Duke Math. J. 140 (2007), p. 165-202. | DOI | MR | Zbl
, & -[45] Minimal-mass blowup solutions of the mass-critical NLS, Forum Math. 20 (2008), p. 881-919. | MR | Zbl
, & ,[46] The defocusing energy-critical nonlinear Schrödinger equation in higher dimensions, Duke Math. J. 138 (2007), p. 281-374. | DOI | MR | Zbl
-[47] Nonlinear Schrödinger equations and sharp interpolation estimates, Comm. Math. Phys. 87 (1982/83), p. 567-576. | DOI | MR | Zbl
-