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Currently displaying 1 – 2 of 2

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Diophantine conditions in global well-posedness for coupled KdV-type systems.

Oh, Tadahiro — 2009

Electronic Journal of Differential Equations (EJDE) [electronic only]

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

Andrea R. Nahmod; Tadahiro Oh; Luc Rey-Bellet; Gigliola Staffilani — 2012

Journal of the European Mathematical Society

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 $ℱ L^{s, r} (T)$ with $s \geq \frac{1}{2}, 2 < r < 4, (s - 1) r < - 1$ and scaling like $H^{\frac{1}{2} - ϵ} (𝕋)$ , for small $ϵ > 0$ . We also show the invariance of this measure.

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