On the Cauchy problem of a new integrable two-component Novikov equation

This paper is devoted to a new integrable two-component Novikov equation with Lax pairs and bi-Hamiltonian structures. Ons the one hand, based on a generalized Ovsyannikov type theorem, we prove the existence and uniqueness of solutions in the Gevrey-Sobolev spaces with the lower bound of the lifespan, and show the continuity of the data-to-solution map. On the other hand, we prove that the strong solutions maintain corresponding properties at infinity within its lifespan provided the initial data decay exponentially and algebraically, respectively.