Uniform attractors for a weakly damped wave equation with sup-cubic nonlinearity

Abstract The nonautonomous dynamical behavior of a weakly damped wave equation with sup-cubic nonlinearity is considered in H 0 1 ( Ω ) × L 2 ( Ω ) . We first prove the global well-posedness of Shatah–Struwe solutions, then establish the existence of strong uniform attractor for some translation non-compact external forcing. The results are based on the recent extension of Strichartz estimates for the bounded domains.