Differential and Integral Equations

Invariant Gibbs measures and a.s. global well posedness for coupled KdV systems

Abstract

We continue our study of the well-posedness theory of a one-parameter family of coupled KdV-type systems in the periodic setting. When the value of a coupling parameter ${\alpha} \in (0, 4) \setminus \{1\}$, we show that the Gibbs measure is invariant under the flow and the system is globally well posed almost surely on the statistical ensemble, provided that certain Diophantine conditions are satisfied.

Article information

Source
Differential Integral Equations, Volume 22, Number 7/8 (2009), 637-668.

Dates
First available in Project Euclid: 20 December 2012