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

Andrea R. Nahmod; Tadahiro Oh; Luc Rey-Bellet; Gigliola Staffilani

Journal of the European Mathematical Society (2012)

- Volume: 014, Issue: 4, page 1275-1330
- ISSN: 1435-9855

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topNahmod, 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 -

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