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Attractor for the viscous two-component Camassa-Holm equation. (English) Zbl 1239.35143

Summary: We study the attractor for a viscous two-component generalization of the Camassa-Holm equation subject to an external force, where the viscosity term is given by a second order differential operator. The global existence of solution to the viscous two-component Camassa-Holm equation with the periodic boundary condition is studied. We obtain the compact and bounded absorbing set and the existence of the global attractor in \(H^{2}\times H^{2}\) for the viscous two-component Camassa-Holm equation by uniform prior estimate and many inequalities.

MSC:

35Q53 KdV equations (Korteweg-de Vries equations)
35B41 Attractors
35A01 Existence problems for PDEs: global existence, local existence, non-existence
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