Well-posedness and attractors for a super-cubic weakly damped wave equation with H−1 source term

This work is devoted to Dirichlet problem for the sup-cubic semi-linear wave equation with H−1 forcing in a bounded domain of R3. The global well-posedness of the weak solution with some translational regularity is obtained. Moreover, the existence of a global attractor as well as exponential attractor in the natural phase space are also considered. The results are crucially based on the Strichartz estimates for the linear wave equation in bounded domain of R3.