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

2010/07/09 by Nahmod, Andrea, Oh, Tadahiro, Rey-Bellet, Luc +1 · 3 citations
#Analysis of PDEs (math.AP) #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1007.1502

Abstract

In this paper 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 FL^s,r(\T) with s ≥ (1)/(2), 2 < r < 4, (s-1)r 0. We also show the invariance of this measure.

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