Global existence of weak solutions to a weakly dissipative modified two‐component Dullin–Gottwald–Holm system

We consider a weakly dissipative modified two-component Dullin–Gottwald–Holm system. The existence of global weak solutions to the system is established. We first give the well-posedness result of viscous approximate problem and obtain the basic energy estimates. Then, we show that the limit of the viscous approximation solutions is a global weak solution to the system. Copyright © 2014 John Wiley & Sons, Ltd.