Differential and Integral Equations

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

Tadahiro Oh

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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

Permanent link to this document
https://projecteuclid.org/euclid.die/1356019542

Mathematical Reviews number (MathSciNet)
MR2532115

Zentralblatt MATH identifier
1240.35477

Subjects
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.)

Citation

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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