A note on the global attractor for weakly damped wave equation

In this short note, we consider the long-time behavior for the solution of weakly damped wave equation with lower regular forcing. The existence of a global attractor is obtained. To verify asymptotic compactness of the semigroup, we present a new method about decomposition of the solution and apply the Strichartz estimate to the wave equation according to the recent progress. Moreover, translational regularity of the attractor is established.