Wave breaking of an integrable Camassa–Holm system with two components

This paper deals with a new integrable two-component Camassa–Holm (CH2) system which describes the motion of fluid. We are concerned with discovering the wave breaking mechanism for the Cauchy problem. Analogous to McKean’s theorem (McKean (1998) [19]) for the Camassa–Holm equation, we establish the sufficient condition on the initial data to guarantee the blow-up of the solution. It turns out that our blow-up theorem is not depend on the initial energy but depend on the sign of initial data y0(x)y0(x) and ρ0(x)ρ0(x).