Global well-posedness and attractors for the hyperbolic Cahn–Hilliard–Oono equation in the whole space
Abstract
We prove the global well-posedness of the so-called hyperbolic relaxation of the Cahn–Hilliard–Oono equation in the whole space ℝ3 with the nonlinearity of the sub-quintic growth rate. Moreover, the dissipativity and the existence of a smooth global attractor in the naturally defined energy space is also verified. The result is crucially based on the Strichartz estimates for the linear Schrödinger equation in ℝ3.
Communicated by F. Brezzi