On Solutions to a Two-Component Generalized Camassa-Holm Equation

摘要

We consider a two-component Camassa-Holm system which arises in shallow water theory. We analyze awave breaking mechanism and the global existence of solutions. First, we discuss the local well posedness and a blow up mechanism, then establish some new blow up criteria for this system formulated either on the line or with space-periodic initial conditions. Finally, the existence of global solutions is analyzed.