Global conservative weak solutions for the two-component Novikov equation

In this paper, we study the existence of global conservative solutions to a two-component Novikov system. The system is an integrable multi-component extension of the Novikov integrable equation. We develop the method of constructing global conservative solutions of the Camassa–Holm equation due to Bressan and Constantin to a two-component case with genuine nonlinear interactions. Our approach is based on the formulation of Bressan and Constantin and additional estimates relating to the new conservation laws of the system.