Global attractor for the weakly damped forced Kawahara equation on the torus

We study the long-time behaviour of solutions for the weakly damped forced Kawahara equation on the torus. More precisely, we prove the existence of a global attractor in (Formula presented.), to which as time passes all solutions draw closer. In fact, we show that the global attractor turns out to lie in a smoother space (Formula presented.) and be bounded therein. Further, we give an upper bound of the size of the attractor in (Formula presented.) that depends only on the damping parameter and the norm of the forcing term.