Invariant weighted Wiener measures and almost sure global well-posedness for the periodic derivative NLS

Nahmod, Andrea R., et al. "Invariant weighted Wiener measures and almost sure global well-posedness for the periodic derivative NLS." Journal of the European Mathematical Society 014.4 (2012): 1275-1330. <http://eudml.org/doc/277560>.

@article{Nahmod2012,
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 $\mathcal \{F\} L^\{s,r\}(\ T)$ with $s\ge \frac\{1\}\{2\},2<r<4, (s-1)r<-1$ and scaling like $H^\{\frac\{1\}\{2\}-\epsilon \}(\mathbb \{T\})$, for small $\epsilon >0$. We also show the invariance of this measure.},
author = {Nahmod, Andrea R., Oh, Tadahiro, Rey-Bellet, Luc, Staffilani, Gigliola},
journal = {Journal of the European Mathematical Society},
keywords = {global-wellposedness; invariant measures; derivative NLS; Wiener measure; well-posedness; invariant measures; derivative NLS; Wiener measure; I-method},
language = {eng},
number = {4},
pages = {1275-1330},
publisher = {European Mathematical Society Publishing House},
title = {Invariant weighted Wiener measures and almost sure global well-posedness for the periodic derivative NLS},
url = {http://eudml.org/doc/277560},
volume = {014},
year = {2012},
}

TY - JOUR
AU - Nahmod, Andrea R.
AU - Oh, Tadahiro
AU - Rey-Bellet, Luc
AU - Staffilani, Gigliola
TI - Invariant weighted Wiener measures and almost sure global well-posedness for the periodic derivative NLS
JO - Journal of the European Mathematical Society
PY - 2012
PB - European Mathematical Society Publishing House
VL - 014
IS - 4
SP - 1275
EP - 1330
AB - 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 $\mathcal {F} L^{s,r}(\ T)$ with $s\ge \frac{1}{2},2<r<4, (s-1)r<-1$ and scaling like $H^{\frac{1}{2}-\epsilon }(\mathbb {T})$, for small $\epsilon >0$. We also show the invariance of this measure.
LA - eng
KW - global-wellposedness; invariant measures; derivative NLS; Wiener measure; well-posedness; invariant measures; derivative NLS; Wiener measure; I-method
UR - http://eudml.org/doc/277560
ER -