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

Voir la notice de l'article provenant de la source EMS Press

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 
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     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},
     publisher = {mathdoc},
     volume = {14},
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     year = {2012},
     doi = {10.4171/jems/333},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/jems/333/}
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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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