Gibbs measure for the periodic derivative nonlinear Schrödinger equation

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.

arXiv commentTo appear in Nonlinearity

References in corpus (4)

• Low regularity local well-posedness of the Derivative Nonlinear Schrödinger Equation with periodic initial data
• Invariant Gibbs Measures and a.s. Global Well-Posedness for Coupled KdV Systems
• Invariant measures for the defocusing NLS
• Long time dynamics for the one dimensional non linear Schrödinger equation