On the Global Well-Posedness of the Viscous Two-Component Camassa-Holm System

Abstract

We establish the local well-posedness for the viscous two-component Camassa-Holm system. Moreover, applying the energy identity, we obtain a globalexistence result for the system with $\left(u_0,{\eta }_0\right)\in H^1\left(ℝ\right)\times L^2\left(ℝ\right)$.