Invariant weighted Wiener measures and almost sure global well-posedness for the periodic derivative NLS
Andrea R. Nahmod, Tadahiro Oh, Luc Rey-Bellet, Gigliola Staffilani (2012)
Journal of the European Mathematical Society
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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.