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 with , , and scaling like for small . We also show the invariance of this measure.
Cite this article
Andrea R. Nahmod, Tadahiro Oh, Luc Rey-Bellet, Gigliola Staffilani, Invariant weighted Wiener measures and almost sure global well-posedness for the periodic derivative NLS. J. Eur. Math. Soc. 14 (2012), no. 4, pp. 1275–1330DOI 10.4171/JEMS/333