Semi-classical limit of Schr??dinger???Poisson equations in space dimension <mml:math altimg="si1.gif" overflow="scroll" xmlns:xocs="http://www.elsevier.com/xml/xocs/dtd" xmlns:xs="http://www.w3.org/2001/XMLSchema" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns="http://www.elsevier.com/xml/ja/dtd" xmlns:ja="http://www.elsevier.com/xml/ja/dtd" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:tb="http://www.elsevier.com/xml/common/table/dtd" xmlns:sb="http://www.elsevier.com/xml/common/struct-bib/dtd" xmlns:ce="http://www.elsevier.com/xml/common/dtd" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:cals="http://www.elsevier.com/xml/common/cals/dtd"><mml:mi>n</mml:mi><mml:mo>???</mml:mo><mml:mn>3</mml:mn></mml:math>, Journal of Differential Equations, vol.233, issue.1, pp.241-275, 2007. ,
DOI : 10.1016/j.jde.2006.10.003
Super-critical geometric optics for nonlinear Schrödinger equations , preprint: arXiv:0704, 2488. ,
Global existence for defocusing cubic NLS and Gross???Pitaevskii equations in three dimensional exterior domains, Journal de Math??matiques Pures et Appliqu??es, vol.89, issue.4 ,
DOI : 10.1016/j.matpur.2007.12.006
Travelling waves for the Gross-Pitaevskii equation. I, Ann, Inst. H. Poincaré Phys. Théor, vol.70, issue.2, pp.147-238, 1999. ,
URL : https://hal.archives-ouvertes.fr/hal-00187672
convergence of the vlasov-poisson system to the incompressible euler equations, Communications in Partial Differential Equations, vol.230, issue.3-4, pp.3-4, 2000. ,
DOI : 10.1016/0022-0396(92)90033-J
Geometric Optics and Instability for Semi-Classical Schr??dinger Equations, Archive for Rational Mechanics and Analysis, vol.61, issue.38, pp.525-553, 2007. ,
DOI : 10.1007/s00205-006-0017-5
WKB Analysis for Nonlinear Schr??dinger Equations with Potential, Communications in Mathematical Physics, vol.202, issue.1, pp.195-221, 2007. ,
DOI : 10.1007/s00220-006-0077-2
Some singular limits for evolutionary Ginzburg-Landau equations, Asymptotic Anal, pp.361-372, 1996. ,
Theory of Bose-Einstein condensation in trapped gases, Reviews of Modern Physics, vol.71, issue.3, pp.463-512, 1999. ,
DOI : 10.1103/RevModPhys.71.463
Schrödinger group on Zhidkov spaces, Adv. Differential Equations, vol.9, issue.5-6, pp.509-538, 2004. ,
The Cauchy problem for defocusing nonlinear Schrödinger equations with nonvanishing initial data at infinity ,
Atomic Bose-Einstein condensation with three-body interactions and collective excitations, Journal of Physics B: Atomic, Molecular and Optical Physics, vol.33, issue.19, pp.4053-4067, 2000. ,
DOI : 10.1088/0953-4075/33/19/316
A review of dispersive limits of (non)linear Schrödinger-type equations, Taiwanese J. Math, vol.4, issue.4, pp.501-529, 2000. ,
Remarques sur l'analyse semi-classique de l'´ equation de Schrödinger non linéaire, Séminaire sur lesÉquationsles´lesÉquations aux Dérivées Partielles, ´ Ecole polytech. Exp. No. XIII, 1992. ,
The Cauchy problem for the Gross???Pitaevskii equation, Annales de l'Institut Henri Poincare (C) Non Linear Analysis, vol.23, issue.5, pp.765-779, 2006. ,
DOI : 10.1016/j.anihpc.2005.09.004
Semiclassical limit of the nonlinear Schrödinger equation in small time, Proc. Amer, pp.523-530, 1998. ,
Nonlinear aspects of the theory of Bose-Einstein condensates, Nonlinearity, vol.14, issue.5, pp.25-62, 2001. ,
DOI : 10.1088/0951-7715/14/5/201
Sharp estimates for pseudo-differential operators with symbols of limited smoothness and commutators, Journal of Functional Analysis, vol.232, issue.2, pp.495-539, 2006. ,
DOI : 10.1016/j.jfa.2005.07.003
Semiclassical Limit of the Gross-Pitaevskii Equation in an Exterior Domain, Archive for Rational Mechanics and Analysis, vol.15, issue.1, pp.79-107, 2005. ,
DOI : 10.1007/s00205-005-0383-4
Compressible fluid flow and systems of conservation laws in several space variables, Applied Mathematical Sciences, vol.53, 1984. ,
DOI : 10.1007/978-1-4612-1116-7
Remarks on the well-posedness of the nonlinear Cauchy problem, Contemp. Math, vol.368, pp.337-356, 2005. ,
DOI : 10.1090/conm/368/06790
Liquid light condensates, Physical Review E, vol.65, issue.6, p.66604, 2002. ,
DOI : 10.1103/PhysRevE.65.066604
Bose-Einstein condensation, International Series of Monographs on Physics, vol.116, 2003. ,
Formation of singularities in three-dimensional compressible fluids, Communications in Mathematical Physics, vol.86, issue.4, pp.475-485, 1985. ,
DOI : 10.1007/BF01210741
Instabilities for supercritical Schrödinger equations in analytic manifolds, preprint ,
The Cauchy problem for a nonlinear Schrödinger equation, JINR Commun, pp.5-87, 1987. ,
Korteweg-de Vries and nonlinear Schrödinger equations: qualitative theory, Lecture Notes in Mathematics, vol.1756, 2001. ,