Gibbs measure for the periodic derivative nonlinear Schrödinger equation

2010/01/24 by Laurent Thomann, Nikolay Tzvetkov, Thomann, Laurent +1 · 4 citations
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Quantum chaos and dynamical systems #advanced mathematical theories

paper · doi:10.48550/arxiv.1001.4269

openalex publication_date 2010/01/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we construct a Gibbs measure for the derivative Schrödinger equation on the circle. The construction uses some renormalisations of Gaussian series and Wiener chaos estimates, ideas which have already been used by the second author in a work on the Benjamin-Ono equation.

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• Probabilistic well-posedness of dispersive PDEs beyond variance blowup I: Benjamin-Bona-Mahony equation
• Quantitative quasi-invariance of Gaussian measures below the energy level for the 1D generalized nonlinear Schrödinger equation and application to global well-posedness

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