Construction of blowup solutions for the nonlinear Schrödinger equation with critical nonlinearity
Jean Bourgain, W. Wang (1997)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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Jean Bourgain, W. Wang (1997)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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Ricardo Pérez-Marco (2001-2002)
Séminaire Bourbaki
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Wei-Min Wang (2004-2005)
Séminaire Équations aux dérivées partielles
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Massimiliano Berti (2011-2012)
Séminaire Laurent Schwartz — EDP et applications
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The aim of this talk is to present some recent existence results about quasi-periodic solutions for PDEs like nonlinear wave and Schrödinger equations in , , and the - derivative wave equation. The proofs are based on both Nash-Moser implicit function theorems and KAM theory.
Dario Bambusi (2000)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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Merle, Frank (1998)
Documenta Mathematica
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Nicolas Burq, Laurent Thomann, Nikolay Tzvetkov (2013)
Annales de l’institut Fourier
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In this article, we first present the construction of Gibbs measures associated to nonlinear Schrödinger equations with harmonic potential. Then we show that the corresponding Cauchy problem is globally well-posed for rough initial conditions in a statistical set (the support of the measures). Finally, we prove that the Gibbs measures are indeed invariant by the flow of the equation. As a byproduct of our analysis, we give a global well-posedness and scattering result for the critical...
Patrick Gérard, Vittoria Pierfelice (2010)
Bulletin de la Société Mathématique de France
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We prove two new results about the Cauchy problem in the energy space for nonlinear Schrödinger equations on four-dimensional compact manifolds. The first one concerns global well-posedness for Hartree-type nonlinearities and includes approximations of cubic NLS on the sphere as a particular case. The second one provides, in the case of zonal data on the sphere, local well-posedness for quadratic nonlinearities as well as a necessary and sufficient condition of global well-posedness...
Herbert Koch (2011-2012)
Séminaire Laurent Schwartz — EDP et applications
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We consider the cubic Nonlinear Schrödinger Equation (NLS) and the Korteweg-de Vries equation in one space dimension. We prove that the solutions of NLS satisfy a-priori local in time bounds in terms of the size of the initial data for (joint work with D. Tataru, [, ]) , and the solutions to KdV satisfy global a priori estimate in (joint work with T. Buckmaster []).