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The Cauchy problem for a dissipative periodic 2-component Degasperis-Procesi system. (English) Zbl 1442.35395

Summary: 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.

MSC:

35Q53 KdV equations (Korteweg-de Vries equations)
35G25 Initial value problems for nonlinear higher-order PDEs
35Q35 PDEs in connection with fluid mechanics
76B15 Water waves, gravity waves; dispersion and scattering, nonlinear interaction
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