Invariant measures for the defocusing NLS

Abstract

We prove the existence and the invariance of a Gibbs measure associated to the defocusing sub-quintic Nonlinear Schroedinger equations on the disc of the plane ${\mathbb{R}}^2$. We also prove an estimate giving some intuition to what may happen in 3 dimensions.

to appear in Annales de l'Institut Fourier

Cited by in corpus (8)

• Long time dynamics for the one dimensional non linear Schrödinger equation
• Invariant measure for a three dimensional nonlinear wave equation
• Probabilistic methods for discrete nonlinear Schrödinger equations
• Low regularity for a quadratic Schrödinger equation on the circle
• Random data Cauchy problem for supercritical Schrödinger equations
• Solitons and Gibbs measures for nonlinear Schroedinger equations
• Invariance of the Gibbs Measure for the Schrodinger-Benjamin-Ono System
• Gibbs measure for the periodic derivative nonlinear Schrödinger equation