Geodesic
Invariant weighted Wiener measures and almost sure global well-posedness for the periodic derivative NLS
Journal of the European Mathematical Society, Tome 14 (2012) no. 4, pp. 1275-1330 Cet article a éte moissonné depuis la source EMS Press

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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 FLs,r(T) with s≥21​, 24, (s−1)r−1 and scaling like H21​−ε(T), for small ε>0. We also show the invariance of this measure.
DOI : 10.4171/jems/333
Classification : 35-XX, 37-XX, 00-XX
Keywords: Global-wellposedness, invariant measures 
@article{JEMS_2012_14_4_a8,
     author = {Andrea R. Nahmod and Tadahiro Oh and Luc Rey-Bellet and Gigliola Staffilani},
     title = {Invariant weighted {Wiener} measures and  almost sure global well-posedness  for the periodic derivative {NLS}},
     journal = {Journal of the European Mathematical Society},
     pages = {1275--1330},
     year = {2012},
     volume = {14},
     number = {4},
     doi = {10.4171/jems/333},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/jems/333/}
}
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%A Luc Rey-Bellet
%A Gigliola Staffilani
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%J Journal of the European Mathematical Society
%D 2012
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%F JEMS_2012_14_4_a8
Andrea R. Nahmod; Tadahiro Oh; Luc Rey-Bellet; Gigliola Staffilani. Invariant weighted Wiener measures and  almost sure global well-posedness  for the periodic derivative NLS. Journal of the European Mathematical Society, Tome 14 (2012) no. 4, pp. 1275-1330. doi: 10.4171/jems/333

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