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Global attractor for a viscous generalized two-component Camassa-Holm equation

Dajin Liu

Abstract


In this paper we study the Cauchy problem for a generalized two-component Camassa-Holm system. We first establish locally well-posed for the new system. Applying the energy estimates, we present two precise blow-up scenarios for this problem. By the conservation of symmetry of the solution to this system, we obtain a blow-up result for strong solutions. Finally, by the method of Lyapunov functions, we find a sufficient condition for global solutions.

Keywords


Generalized two-component Camassa-Holm equation, viscous, global attractor.

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