Invariant weightedWiener measures and almost sure global well-posedness for the periodic derivative NLS

Abstract

We construct an invariant weighted Wiener measure associated to the periodic derivative nonlinear Schrödinger equation in one dimension and establish global well-posedness for data living in its support. In particular almost surely for data in a Fourier-Lebesgue space FLs;r .T/ with s ≥ 1=2, 2 < r < 4, .s - 1/r 0. We also show the invariance of this measure.