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

Original manuscript July 9, 2010We 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 FL[superscript s,r](\T) with s ≥ 1/2, 2 0. We also show the invariance of this measure.National Science Foundation (U.S.) (DMS 0803160)Radcliffe Institute for Advanced Study (Fellowship)National Science Foundation (U.S.) (DMS 0602678