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 α ∈ (0, 4) 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.
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