Existence and uniqueness of the global conservative weak solutions to the rotation-Camassa–Holm equation

Abstract We study herein the Camassa–Holm-type equation, which can be considered as a model in the shallow water for the long-crested waves propagating near the equator with effect of the Coriolis force due to the Earth's rotation. This quasi-linear equation is nonlocal with higher-order nonlinearities compared to the classical Camassa–Holm equation. We establish the global existence and uniqueness of the energy conservative weak solutions in the energy space H 1 to this model equation.