Strong attractors for weakly damped quintic wave equation in bounded domains

In this paper, we study the longtime dynamics for the weakly damped wave equation with quintic non-linearity in a bounded smooth domain of ${\mathbb{R}}^3\mathrm{.}$ Based on the Strichartz estimates for the case of bounded domains, we establish the existence of a strong global attractor in the phase space $H^2(\mathrm{\Omega })\cap H_0^1(\mathrm{\Omega })\times H_0^1(\mathrm{\Omega })$. Moreover, the finite fractal dimension of the attractor is also shown with the help of the quasi-stable estimation.