On the Cauchy problem for the new integrable two-component Novikov equation (Q2183519)

A new integrable two-component Novikov equation was derived by \textit{H. Li} [J. Nonlinear Math. Phys. 26, No. 3, 390--403 (2019; Zbl 1417.37231)]. This system has the Lax pair formulation and can be expressed as a bi-Hamiltonian system. The authors prove the local well-posedness of the two-component Novikov system in nonhomogeneous Besov spaces. They use the Littlewood-Paley theory and analysis of the transport equations. Then, the authors verify that the blow-up may only occur in the form of the wave breaking implying that the solutions remain bounded but their first derivative may become unbounded in a finite time. For analytic initial data, the unique solutions to the Cauchy problem remain analytic in both variables, globally in space and locally in time. Finally, the authors prove that if the initial data decay exponentially or algebraically at infinity, the strong solutions of the two-component Novikov system also decay exponentially or algebraically at infinity within its lifespan.