Invariant weighted Wiener measures and almost sure global well-posedness for the periodic derivative NLS
Author(s)Nahmod, Andrea; Oh, Tadahiro; Rey-Bellet, Luc; Staffilani, Gigliola
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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 FL[superscript s,r](\T) with s ≥ 1/2, 2 < r < 4, (s−1)r < −1 and scaling like H1/2[superscript −ϵ](T), for small ϵ>0. We also show the invariance of this measure.
Original manuscript July 9, 2010
DepartmentMassachusetts Institute of Technology. Department of Mathematics
Journal of the European Mathematical Society
European Mathematical Society Publishing House
Nahmod, Andrea, Tadahiro Oh, Luc Rey-Bellet, and Gigliola Staffilani. “Invariant weighted Wiener measures and almost sure global well-posedness for the periodic derivative NLS.” Journal of the European Mathematical Society (2012): 1275-1330.