@incollection{AST_2013__352__355_0, author = {Lannes, David}, title = {Space time resonances [after {Germain,} {Masmoudi,} {Shatah]}}, booktitle = {S\'eminaire Bourbaki volume 2011/2012 expos\'es 1043-1058}, series = {Ast\'erisque}, note = {talk:1053}, pages = {355--388}, publisher = {Soci\'et\'e math\'ematique de France}, number = {352}, year = {2013}, mrnumber = {3087351}, zbl = {1304.35006}, language = {en}, url = {http://www.numdam.org/item/AST_2013__352__355_0/} }
TY - CHAP AU - Lannes, David TI - Space time resonances [after Germain, Masmoudi, Shatah] BT - Séminaire Bourbaki volume 2011/2012 exposés 1043-1058 AU - Collectif T3 - Astérisque N1 - talk:1053 PY - 2013 SP - 355 EP - 388 IS - 352 PB - Société mathématique de France UR - http://www.numdam.org/item/AST_2013__352__355_0/ LA - en ID - AST_2013__352__355_0 ER -
%0 Book Section %A Lannes, David %T Space time resonances [after Germain, Masmoudi, Shatah] %B Séminaire Bourbaki volume 2011/2012 exposés 1043-1058 %A Collectif %S Astérisque %Z talk:1053 %D 2013 %P 355-388 %N 352 %I Société mathématique de France %U http://www.numdam.org/item/AST_2013__352__355_0/ %G en %F AST_2013__352__355_0
Lannes, David. Space time resonances [after Germain, Masmoudi, Shatah], in Séminaire Bourbaki volume 2011/2012 exposés 1043-1058, Astérisque, no. 352 (2013), Talk no. 1053, 34 p. http://www.numdam.org/item/AST_2013__352__355_0/
[1] Blowup of small data solutions for a quasilinear wave equation in two space dimensions", Ann. of Math. 149 (1999), no. 1, p. 97-127. | DOI | EuDML | MR | Zbl
- "[2] A general framework for diffractive optics and its applications to lasers with large spectrums and short pulses", SIAM J. Math. Anal. 34 (2002), no. 3, p. 636-674. | DOI | MR | Zbl
& - "[3] Global solutions of nonlinear hyperbolic equations for small initial data", Comm. Pure Appl. Math. 39 (1986), no. 2, p. 267-282. | DOI | MR | Zbl
- "[4] The global nonlinear stability of the Minkowski space, Princeton Mathematical Series, vol. 41, Princeton Univ. Press, 1993. | MR | Zbl
& -[5] Rigorous derivation of the nonlinear Schrödinger equation and Davey-Stewartson systems from quadratic hyperbolic systems", Asymptot. Anal. 31 (2002), no. 1, p. 69-91. | MR | Zbl
- "[6] Hamiltonian long-wave approximations to the water-wave problem", Wave Motion 19 (1994), no. 4, p. 367-389. | DOI | MR | Zbl
& - "[7] Numerical simulation of gravity waves", J. Comput. Phys. 108 (1993), no. 1, p. 73-83. | DOI | MR | Zbl
& - "[8] A new physical-space approach to decay for the wave equation with applications to black hole spacetimes", in XVIth International Congress on Mathematical Physics, World Sci. Publ., Hackensack, NJ, 2010, p. 421-432. | DOI | MR | Zbl
& - "[9] Existence globale et comportement asymptotique pour l'équation de Klein-Gordon quasi linéaire à données petites en dimension ", Ann. Sci. École Norm. Sup. 34 (2001), no. 1, p. 1-61. | DOI | EuDML | Numdam | MR | Zbl
- "[9] Existence globale et comportement asymptotique pour l'équation de Klein-Gordon quasi linéaire à données petites en dimension ", erratum: Ann. Sci. École Norm. Sup. 39 (2006), 335-345. | DOI | EuDML | Numdam | MR | Zbl
- "[10] Diffractive nonlinear geometric optics", in Séminaire sur les Équations aux Dérivées Partielles, 1995-1996, Sémin. Équ. Dériv. Partielles, École Polytech., 1996, exp. n° XVII. | EuDML | Numdam | MR | Zbl
, , & - "[11] Decay estimates for hyperbolic systems", Hokkaido Math. J. 33 (2004), no. 1, p. 83-113. | DOI | MR | Zbl
, & - "[12] Global solutions for coupled Klein-Gordon equations with different speeds", to appear in Ann. Inst. Fourier. | Numdam | MR | Zbl
- "[13] Global existence for the Euler-Maxwell system", submitted. | DOI | MR | Zbl
& - "[14] Global solutions for quadratic Schrödinger equations", Int. Math. Res. Not. 2009 (2009), no. 3, p. 414-432. | MR | Zbl
, & - "[15] Global solutions for quadratic Schrödinger equations", J. Math. Pures Appl. 97 (2012), no. 5, p. 505-543. | DOI | MR | Zbl
, "[16] Global solutions for the gravity water waves equation in dimension ", Ann. of Math. 175 (2012), no. 2, p. 691-754. | DOI | MR | Zbl
, "[17] Global dispersive solutions for the Gross-Pitaevskii equation in two and three dimensions", Ann. Henri Poincaré 8 (2007), no. 7, p. 1303-1331. | DOI | MR | Zbl
, & - "[18] Scattering theory for the Gross-Pitaevskii equation in three dimensions", Commun. Contemp. Math. 11 (2009), no. 4, p. 657-707. | DOI | MR | Zbl
, & , "[19] Applications bilinéaires compatibles avec un opérateur hyperbolique", Ann. Inst. H. Poincaré Anal. Non Linéaire 4 (1987), no. 4, p. 357-376. | DOI | EuDML | Numdam | MR | Zbl
& - "[20] Asymptotics for large time of solutions to the nonlinear Schrödinger and Hartree equations", Amer. J. Math. 120 (1998), no. 2, p. 369-389. | DOI | MR | Zbl
& - "[21] Lectures on nonlinear hyperbolic differential equations, Mathématiques & Applications, vol. 26, Springer, 1997. | MR | Zbl
-[22] Blow-up for quasilinear wave equations in three space dimensions", Comm. Pure Appl. Math. 34 (1981), no. 1, p. 29-51. | DOI | MR | Zbl
- "[23] Diffractive nonlinear geometric optics with rectification", Indiana Univ. Math. J. 47 (1998), no. 4, p. 1167-1241. | MR | Zbl
, & - "[24] Transparent nonlinear geometric optics and Maxwell-Bloch equations", J. Differential Equations 166 (2000), no. 1, p. 175-250. | DOI | MR | Zbl
, & , "[25] Uniform decay estimates and the Lorentz invariance of the classical wave equation", Comm. Pure Appl. Math. 38 (1985), no. 3, p. 321-332. | DOI | MR | Zbl
- "[26] The null condition and global existence to nonlinear wave equations", in Nonlinear systems of partial differential equations in applied mathematics, Part 1 (Santa Fe, N.M., 1984), Lectures in Appl. Math., vol. 23, Amer. Math. Soc., 1986, p. 293-326. | MR | Zbl
, "[27] Linear stability of black holes (d'après M. Dafermos et I. Rodnianski)", Séminaire Bourbaki, vol. 2009/2010, exposé n° 1015, Astérisque 339 (2011), p. 91-135. | Numdam | MR | Zbl
, "[28] Smoothing estimates for null forms and applications", Int. Math. Res. Not. 1994 (1994), no. 9, p. 383-390. | DOI | MR | Zbl
& - "[29] Dispersive effects for nonlinear geometrical optics with rectification", Asymptot. Anal. 18 (1998), nos. 1-2, p. 111-146. | MR | Zbl
- "[30] Global existence for the Einstein vacuum equations in wave coordinates", Comm. Math. Phys. 256 (2005), no. 1, p. 43-110. | DOI | MR | Zbl
& - "[31] Almost global existence of solutions for the quadratic semilinear Klein-Gordon equation in one space dimension", Funkcial. Ekvac. 40 (1997), no. 2, p. 313-333. | MR | Zbl
, & - "[32] Compacité par compensation: condition nécessaire et suffisante de continuité faible sous une hypothèse de rang constant", Ann. Scuola Norm. Sup. Pisa Cl. Sci. 8 (1981), no. 1, p. 69-102. | EuDML | Numdam | MR | Zbl
- "[33] Global existence and asymptotic behavior of solutions for the Klein-Gordon equations with quadratic nonlinearity in two space dimensions", Math. Z. 222 (1996), no. 3, p. 341-362. | DOI | EuDML | MR | Zbl
, & - "[34] Normal forms and quadratic nonlinear Klein-Gordon equations", Comm. Pure Appl. Math. 38 (1985), no. 5, p. 685-696. | DOI | MR | Zbl
- "[35] Geometry and a priori estimates for free boundary problems of the Euler equation", Comm. Pure Appl. Math. 61 (2008), no. 5, p. 698-744. | DOI | MR | Zbl
& - "[36] A wave operator for a nonlinear Klein-Gordon equation", Lett. Math. Phys. 7 (1983), no. 5, p. 387-398. | DOI | MR | Zbl
- "[37] The Cauchy problem for nonlinear Klein-Gordon equations", Comm. Math. Phys. 152 (1993), no. 3, p. 433-478. | DOI | MR | Zbl
& - "[38] Lectures on non-linear wave equations, International Press, 2008. | MR | Zbl
-[39] Nonlinear scattering theory at low energy", J. Funct. Anal. 41 (1981), no. 1, p. 110-133. | DOI | MR | Zbl
- "[40] Compensated compactness and applications to partial differential equations", in Nonlinear analysis and mechanics: Heriot-Watt Symposium, Vol. IV, Res. Notes in Math., vol. 39, Pitman, 1979, p. 136-212. | MR | Zbl
- "[41] Well-posedness in Sobolev spaces of the full water wave problem in ", Invent. Math. 130 (1997), no. 1, p. 39-72. | DOI | MR | Zbl
- "[42] Well-posedness in Sobolev spaces of the full water wave problem in ", J. Amer. Math. Soc. 12 (1999), no. 2, p. 445-495. | DOI | MR | Zbl
, "[43] Almost global wellposedness of the full water wave problem", Invent. Math. 177 (2009), no. 1, p. 45-135. | DOI | Zbl
, "[44] Global wellposedness of the full water wave problem", Invent. Math. 184 (2011), no. 1, p. 125-220. | DOI | Zbl
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