Existence and uniqueness of the global conservative weak solutions to the cubic Camassa-Holm-Type equation

This paper is devoted to the cubic Camassa-Holm-Type equation with a nonlocal cubic nonlinearity suggested as an asymptotic model for the 2D full water wave dynamics which 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 solution in the energy space.