Global attractor of a wave equation with Hardy potentials and nonlinear damping

In this paper, we consider the well-posedness and long-time behavior of a wave equation that includes memory term, Hardy potentials and nonlinear damping. We first prove the well-posedness of the problem based on the semigroup method for 0 ≤ λ < (1 − δ1)λ*. Under the assumption on the growth of the nonlinear damping at infinity, but we do not impose any condition on the degeneracy at origin, the existence of a global attractor is obtained by proving the existence of a strict Lyapunov functional and the asymptotical smoothness of the semigroup. When the nonlinear damping is non-degenerate at origin, we establish a quasi-stability inequality, which implies the fractal dimension of the global attractor is finite under an extra assumption on the nonlinear damping.