Invariance of the white noise for KdV

Abstract

We prove the invariance of the mean 0 white noise for the periodic KdV. First, we show that the Besov-type space \hat{b}^s_{p, \infty}, sp <-1, contains the support of the white noise. Then, we prove local well-posedness in \hat{b}^s_{p, \infty} for p= 2+, s = -{1/2}+ such that sp <-1. In establishing the local well-posedness, we use a variant of the Bourgain spaces with a weight. This provides an analytical proof of the invariance of the white noise under the flow of KdV obtained in Quastel-Valko.

18 pages. To appear in Comm. Math. Phys

References in corpus (2)

• Invariant Gibbs Measures and a.s. Global Well-Posedness for Coupled KdV Systems
• Invariant measure for a three dimensional nonlinear wave equation

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