Invariant Gibbs Measures and a.s. Global Well-Posedness for Coupled KdV Systems

Details Invariant Gibbs Measures and a.s. Global Well-Posedness for Coupled KdV Systems Invariant Gibbs Measures and a.s. Global Well-Posedness for Coupled KdV Systems

2009-04-19

arxiv.org/abs/0904.2816v1

Mathematics

Analysis of PDEs

19 pages. To appear in Diff. Integ. Eqns

Scientific paper

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.

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