On the global existence and wave-breaking criteria for the two-component Camassa–Holm system

Considered herein is a two-component Camassa–Holm system modeling shallow water waves moving over a linear shear flow. A wave-breaking criterion for strong solutions is determined in the lowest Sobolev space Hs , s > 32 by using the localization analysis in the transport equation theory. Moreover, an improved result of global solutions with only a nonzero initial profile of the free surface component of the system is established in this Sobolev space Hs . © 2010 Elsevier Inc. All rights reserved.