The dissipative periodic 2-component Degasperis-Procesi system is investigated. A local well-posedness for the system in Besov space is established by using the Littlewood-Paley theory and a priori estimates for the solutions of transport equation. The wave-breaking criterions for strong solutions to the system with certain initial data are derived.
"The Cauchy Problem for a Dissipative Periodic 2-Component Degasperis-Procesi System." J. Appl. Math. 2014 1 - 17, 2014. https://doi.org/10.1155/2014/410981