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.