  In this paper, we study the long-time dynamics for the wave equation with
nonlocal weak damping and sup-cubic nonlinearity in a bounded smooth domain of
$\mathbb{R}^3.$ Based on the Strichartz estimates for the case of bounded
domains, we first prove the global well-posedness of the Shatah-Struwe
solutions. Then we establish the existence of the global attractor for the
Shatah-Struwe solution semigroup by the method of contractive function.
Finally, we verify the existence of a polynomial attractor for this semigroup.
