20 07 Invariant Measures for the Defocusing Nls
نویسنده
چکیده
We prove the existence and the invariance of a Gibbs measure associated to the defocusing sub-quintic Nonlinear Schrödinger equations on the disc of the plane R 2. We also prove an estimate giving some intuition to what may happen in 3 dimensions. Résumé. On démontre l'existence et l'invariance d'une mesure de Gibbs par le flot de l'´ equation de Schrödinger non linéaire posée sur le disque du plan R 2. On démontré egalement une estimée qui donne une idée de ce qui pourrait arriver en dimension 3.
منابع مشابه
From Bosonic Grand-canonical Ensembles to Nonlinear Gibbs Measures
In a recent paper, in collaboration with Mathieu Lewin and Phan Thành Nam, we showed that nonlinear Gibbs measures based on Gross-Pitaevskii like functionals could be derived from many-body quantum mechanics, in a mean-field limit. This text summarizes these findings. It focuses on the simplest, but most physically relevant, case we could treat so far, namely that of the defocusing cubic NLS fu...
متن کاملJ ul 2 00 7 INVARIANT MEASURES FOR THE DEFOCUSING NLS
We prove the existence and the invariance of a Gibbs measure associated to the defocusing sub-quintic Nonlinear Schrödinger equations on the disc of the plane R 2. We also prove an estimate giving some intuition to what may happen in 3 dimensions. Résumé. On démontre l'existence et l'invariance d'une mesure de Gibbs par le flot de l'´ equation de Schrödinger non linéaire posée sur le disque du ...
متن کاملA pr 2 00 8 INVARIANT MEASURES FOR THE DEFOCUSING NLS
We prove the existence and the invariance of a Gibbs measure associated to the defocusing sub-quintic Nonlinear Schrödinger equations on the disc of the plane R 2. We also prove an estimate giving some intuition to what may happen in 3 dimensions. Résumé. On démontre l'existence et l'invariance d'une mesure de Gibbs par le flot de l'´ equation de Schrödinger non linéaire posée sur le disque du ...
متن کاملNumerical Simulations of the Energy- Supercritical Nonlinear Schrödinger Equation
We present numerical simulations of the defocusing nonlinear Schrödinger (NLS) equation with an energy supercritical nonlinearity. These computations were motivated by recent works of Kenig-Merle and Kilip-Visan who considered some energy supercritical wave equations and proved that if the solution is a priori bounded in the critical Sobolev space (i.e. the space whose homogeneous norm is invar...
متن کاملNon - Focusing Instabilities in Coupled ,
The nonlinear coupling of two scalar nonlinear Schrr odinger (NLS) elds results in non-focusing instabilities that exist independently of the well-known modulational instability of the focusing NLS equation. The focusing versus defocusing behavior of scalar NLS elds is a well-known model for the corresponding behavior of pulse transmission in optical bers in the anomalous (focusing) versus norm...
متن کامل