The Cauchy problem and blow-up phenomena of a new integrable two-component Camassa–Holm system

This paper considers the Cauchy problem and blow-up phenomena of a new integrable two-component Camassa–Holm system, which is a natural extension of the Fokas–Olver–Rosenau–Qiao equation. Firstly, the local well-posedness of the system in the critical Besov space B2,112(R)×B2,112(R) is investigated, and it is shown that the data-to-solution mapping is Hölder continuous. Then, a blow-up criteria for the Cauchy problem in the critical Besov space is derived. Moreover, with conditions on the initial data, a new blow-up criteria is obtained by virtue of the blow-up criteria at hand and the conservative property of mm and nn along the characteristics. Finally, a global existence result for the strong solution is established.