Invariant weighted Wiener measures and almost sure global well-posedness for the periodic derivative NLS
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Staffilani_Invariant weighted.pdf
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Author(s)
Nahmod, Andrea
Oh, Tadahiro
Rey-Bellet, Luc
Staffilani, Gigliola
Date Issued
2012
Journal
Journal of the European Mathematical Society
Publisher
European Mathematical Society Publishing House
Citation
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.
Version
Original manuscript
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 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.
Description
Original manuscript July 9, 2010
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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Creative Commons Attribution-Noncommercial-Share Alike 3.0
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DOI of Published Version
https://doi.org/10.4171/jems/333
