Global Existence and Finite‐Time Blow‐Up for an Integrable Two‐Component Novikov System With Peakons

ABSTRACT This paper is devoted to an integrable two‐component Novikov system with peakons, which is the two‐component generalization of the Novikov equation. The precise blow‐up scenario for the strong solutions to the system is derived. Furthermore, we prove that some initial data develop into global strong solutions to the system, while some certain initial profiles lead to blow‐up strong solutions in finite time.