Wave-breaking phenomena and persistence properties for the nonlocal rotation-Camassa–Holm equation

Abstract

Consideration in the present paper is a mathematical model proposed as an equation of long-crested shallow water waves propagating in one direction with the effect of Earth’s rotation. This model equation is analogous to the Camassa–Holm approximation of the two-dimensional incompressible and irrotational Euler equations, and its solution corresponding to physically relevant initial perturbations is more accurate on a much longer timescale. The effects of the Coriolis force caused by the Earth rotation and nonlocal higher nonlinearities on the blow-up criteria and wave-breaking phenomena in the periodic setting are investigated. Moreover, working with moderate weight functions that are commonly used in time–frequency analysis, some persistence results to the equation are illustrated.