Global well-posedness and attractor for damped wave equation with sup-cubic nonlinearity and lower regular forcing on $\mathbb{R}^3$

Abstract

The dissipative wave equation with sup-cubic nonlinearity and lower regular forcing term which belongs to $H^{-1}({\mathbb{R}^3})$ in the whole space $\mathbb{R}^3$ is considered. Well-posedness of a translational regular solution is achieved by establishing extra space-time translational regularity of an energy solution. Furthermore, a global attractor in the naturally defined energy space $H^1(\mathbb{R}^3)\times L^2(\mathbb{R}^3)$ is built.