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

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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 L 2 , 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 H 2 and be bounded therein. Further, we give an upper bound of the size of the attractor in H 2 that depends only on the damping parameter and the norm of the forcing term.