Abstract
We consider a periodic 2-component Camassa–Holm equation with vorticity in the paper. We first give the local well-posedness and the blow-up criterion for strong solutions to the equation in the Sobolev space Hs, . We then present a global existence result for strong solutions to the equation. We finally obtain several blow-up results and the blow-up rate of strong solutions to the equation. We finally examine the propagation behaviour of compactly supported solutions to the equation. The obtained results cover and improve the earlier results for a periodic 2-component Camssa–Holm equation without vorticity.
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