Well-posedness and blow-up phenomena for an integrable three-component Camassa-Holm system (Q1650479)

In this paper the authors considered the Cauchy problem for an integrable three-component Camassa-Holm system. Their main goal is to study the local well-posedness and blow-up phenomena for this problem. Firstly, they proved the local well-posedness with initial condition in Besov spaces. Then they gave a blow-up criteria by arguing inductively with respect to the regularity index. Finally, they obtained a Riccati-type differential inequality by using the structure of the equation, and, thanks to this, they proved another blow-up criteria with sufficient conditions on initial data.