On the Blow‐Up of Solutions of a Weakly Dissipative Modified Two‐Component Periodic Camassa‐Holm System

Abstract

We study the Cauchy problem of a weakly dissipative modified two-component periodic Camassa-Holm equation. We first establish the local well-posedness result. Then we derive the precise blow-up scenario and the blow-up rate for strong solutions to the system. Finally, we present two blow-up results for strong solutions to the system.