Differential and Integral Equations

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

Tadahiro Oh

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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

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

First available in Project Euclid: 20 December 2012

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35Q53: KdV-like equations (Korteweg-de Vries) [See also 37K10]
Secondary: 35B30: Dependence of solutions on initial and boundary data, parameters [See also 37Cxx] 37A99: None of the above, but in this section 37K10: Completely integrable systems, integrability tests, bi-Hamiltonian structures, hierarchies (KdV, KP, Toda, etc.)


Oh, Tadahiro. Invariant Gibbs measures and a.s. global well posedness for coupled KdV systems. Differential Integral Equations 22 (2009), no. 7/8, 637--668. https://projecteuclid.org/euclid.die/1356019542

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