Well-posedness of a class of solutions to an integrable two-component Camassa-Holm system

In this paper, we study a class of solutions to the Cauchy problem for an integrable two-component Camassa-Holm system with the initial data (u(0), rho(0) - 1) is an element of(H-1(R) boolean AND W-1,W- infinity (R)) x (L-2 (R) boolean AND L-infinity (R)). Based on characteristics, we study a corresponding ODE and obtain a unique local solution by applying the contraction mapping principle. We prove local existence and uniqueness of the solution to the Camassa-Holm system by constructing a solution obtained from the ODE and studying the regularity of the solution. Finally, we show continuous dependence of the solution on the initial data in some weak sense. (C) 2018 Elsevier Inc. All rights reserved.