Blow-up issues for a two-component system modelling water waves with constant vorticity

Considered herein is the blow-up mechanism to the two-component system which models two-dimensional shallow water waves with constant vorticity. We first derive the precise blow-up scenario for strong solutions to the system. Then, we establish the new local-in-space blow-up results simplifying and extending the earlier blow-up criterion for this system. Finally, the propagation speed of strong solutions has been investigated.