Mathematics – Analysis of PDEs
Scientific paper
2010-07-09
Mathematics
Analysis of PDEs
52 pages
Scientific paper
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.
Nahmod Andrea
Oh Tadahiro
Rey-Bellet Luc
Staffilani Gigliola
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