| Abstract: | Considered herein is the persistence property of the solutions to the generalized two-component integrable Dullin–Gottwald–Holm system, which was derived from the Euler equation with nonzero constant vorticity in shallow water waves moving over a linear shear flow. Firstly, the persistence properties of the system are investigated in weighted $$L^p$$-spaces for a large class of moderate weights. Then, we establish the new local-in-space blow-up results simplifying and extending earlier blow-up criterion for this system. |
