We study generalized viscous Cahn–Hilliard problems with nonlinearities satisfying critical
growth conditions in W01, p (Ω), where Ω is a bounded smooth domain in Rn, n⩾ 3. In the
critical growth case, we prove that the problems are locally well posed and obtain a
bootstrapping procedure showing that the solutions are classical. For p= 2 and almost
critical dissipative nonlinearities we prove global well posedness, existence of global
attractors in H01 (Ω) and, uniformly with respect to the viscosity parameter, L∞(Ω) bounds …

We study generalized viscous Cahn-Hilliard problems with nonlinearities satisfying critical
growth conditions in W01, p (Ω), where Ω is a bounded smooth domain in Rn, n≥ 3. In the
critical growth case, we prove that the problems are locally well posed and obtain a
bootstrapping procedure showing that the solutions are classical. For p= 2 and almost
critical dissipative nonlinearities we prove global well posedness, existence of global
attractors in H01 (Ω) and, uniformly with respect to the viscosity parameter, L∞(Ω) bounds …