INVARIANT WEIGHTED WIENER MEASURES AND ALMOST SURE GLOBAL WELL-POSEDNESS FOR THE PERIODIC DERIVATIVE NLS.

By Andrea R. Nahmod, Tadahiro Oh, Luc Rey-Bellet, Gigliola Staffilani. 2010

141 citations recorded by the source corpus.

In this paper we construct an invariant weighted Wiener measure associated to the periodic derivative nonlinear Schrodinger 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 spaceFL s;r (T) with s 1 , 2 0. We also show the invariance of this measure.

View Paper: https://www.semanticscholar.org/paper/319a88d33a018f991c8b33c5a324bc9e2bf4b278

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Citations in the corpus

Almost sure global well-posedness for the energy-critical defocusing nonlinear wave equation on $\mathbb{R}^d$, $d=4$ and $5$ (2014, unknown): “orous by exploiting the invariance of the ﬁnite dimensional Gibbs measures for the associated ﬁnite dimensional approximations of NLS. This approach has been used in subsequent works; see for example [8, 9, 65, 16, 18, 50, 45, 26, 14, 24, 57, 12]. In our context, however, there is no apparent (forma”
Remarks on the Gibbs measures for nonlinear dispersive equations (2014, result): “This result may be seen as a consequence of a recent work by Nahmod, Oh, ReyBellet and Staffilani [33] and Nahmod, Ray-Bellet, Sheffield and Staffilani [34].”
Invariant Measures and Long-Time Behavior for the Benjamin–Ono Equation (2014, background): “See for instance [23] for KdV and [16] for DNLS.”
Almost sure well-posedness for the periodic 3D quintic nonlinear Schr\"odinger equation below the energy space (2013, background): “ain [1, 2, 4] several works have appeared in which the well-posedness theory has been studied from a nondeterministic point of view relying on and adapting probabilistic ideas and tools as well (c.f. [11, 12, 34, 28, 29, 35, 26, 27, 32, 17, 25, 15, 18, 19] and references therein). It is by now well ”