A Study On The Two Component Periodic Shallow Water Systems
Abstract
In this dissertation we study the generalized periodic two-component Camassa-Holm system and the generalized periodic two-component Dullin-Gottwald-Holm system, which can be derived from the Euler equation with nonzero constant vorticity in shallow water waves moving over a linear shear flow. The precise blow-up scenarios of strong solutions and several results of blow-up solutions with certain initial profiles are described in detail. The exact blow-up rates are also determined. Finally, the sufficient conditions for global solutions are established.