- journal article metadata
European Mathematical Society Publishing House
2016-09-19 17:05:07
Journal of the European Mathematical Society
J. Eur. Math. Soc.
JEMS
1435-9855
1435-9863
General
10.4171/JEMS
http://www.ems-ph.org/doi/10.4171/JEMS
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European Mathematical Society Publishing House
Zuerich, Switzerland
© European Mathematical Society
14
2012
4
Invariant weighted Wiener measures and almost sure global well-posedness for the periodic derivative NLS
Andrea
Nahmod
University of Massachusetts, AMHERST, UNITED STATES
Tadahiro
Oh
Princeton University, PRINCETON, UNITED STATES
Luc
Rey-Bellet
University of Massachusetts, AMHERST, UNITED STATES
Gigliola
Staffilani
Massachusetts Institute of Technology, CAMBRIDGE, UNITED STATES
Global-wellposedness, invariant measures
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 $s \ge \frac{1}{2}$, $2 < r < 4$, $(s-1)r 0$. We also show the invariance of this measure.
Partial differential equations
Dynamical systems and ergodic theory
General
1275
1330
10.4171/JEMS/333
http://www.ems-ph.org/doi/10.4171/JEMS/333