Blow-up phemomenon for the 3-component Degasperis-Procesi equation

In this paper, we consider the Cauchy problem of the 3-component Degasperis-Procesi equation. Firstly, we discuss a local well-posedness result and a blow-up criterion in the low besov space. Secondly, we study the blow-up phenomenon by using the method which does not require any conservation law. Finally, we investigate some persistence properties.