Gibbs measure for the periodic derivative nonlinear Schrödinger equation

Laurent Thomann (1) , Nikolay Tzvetkov (2)

1 LMJL - Laboratoire de Mathématiques Jean Leray
2 AGM - UMR 8088 - Analyse, Géométrie et Modélisation

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.

Mots clés: Nonlinear Schrödinger equation; random data; Gibbs measure

Domaines: Equations aux dérivées partielles [math.AP]

Laurent Thomann, Nikolay Tzvetkov. Gibbs measure for the periodic derivative nonlinear Schrödinger equation. Nonlinearity, 2011, 23 (11), pp.2771--2791. ⟨hal-00449963v4⟩