The attractor on viscosity Degasperis–Procesi equation

In this paper the dynamical behaviors of a dispersive shallow water equation with viscosity, viscosity Degasperis–Procesi equation, are investigated. The existence of global solution to viscosity Degasperis–Procesi equation in L2L2 under the periodical boundary condition is studied and the existence of the global attractor of semi-group to solution on viscosity Degasperis–Procesi equation in H2H2 is obtained.