On local-in-space blow-up scenarios for a weakly dissipative rotation-Camassa–Holm equation

ABSTRACT

In this paper, we mainly devote to investigate a weakly dissipative shallow water wave model. By overcoming the difficulties caused by the complicated higher-order nonlinear terms and dissipative term, we present blow-up scenarios with dissipative parameter $\lambda ⩾0$ in the non-periodic case under different initial conditions. Meanwhile, we obtain the blow-up result with $\lambda =0$ in the periodic case.

KEYWORDS:

• Weakly dissipative
• rotation-Camassa–Holm equation
• blow-up criteria

MATHEMATICS SUBJECT CLASSIFICATIONS (2010):

• 35A01
• 35B44
• 35B65
• 35G25

Disclosure statement

No potential conflict of interest was reported by the author.