Existence and regularity of the global attractor for a weakly damped forced shallow water equation in H1image Original Research Article

In this paper we prove the existence of the global attractor for a weakly damped forced shallow water equation in View the MathML sourceH1(R). Moreover, we show that the global attractor is actually compact in View the MathML sourceH4(R). The main method is the combination of the energy equation, a suitable splitting of the solutions, and bilinear estimates in Bourgain spaces.