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Article
Invariant weighted Wiener measures and almost sure global well-posedness for the periodic derivative NLS
JEMS
(2010)
Abstract
In this paper we construct an invariant weighted Wiener measure associated to the periodic derivative nonlinear Schr\"odinger 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 ${\mathcal F}L^{s,r}(\T)$ with $s \ge \frac{1}{2}$, $2 < r < 4$, $(s-1)r <-1$ and scaling like $H^{\frac{1}{2}-\epsilon}(\T),$ for small $\epsilon >0$. We also show the invariance of this measure.
Disciplines
Publication Date
2010
Publisher Statement
This article was harvested from arXiv,
arXiv:1007.1502v1
Citation Information
Andrea Nahmod, Tadahiro Oh, Luc Rey-Bellet and Gigliola Staffilani. "Invariant weighted Wiener measures and almost sure global well-posedness for the periodic derivative NLS" JEMS (2010) Available at: http://works.bepress.com/andrea_nahmod/2/