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We address, in a three-dimensional spatial setting, both the viscous and thestandard Cahn-Hilliard equation with a nonconstant mobility coefficient. As itwas shown in J.W. Barrett and J.W. Blowey, Math. Comp., 68 (1999), 487-517, onecannot expect uniqueness of the solution to the related initial and boundaryvalue problems. Nevertheless, referring to J. Ball's theory of generalizedsemiflows, we are able to prove existence of compact quasi-invariant globalattractors for the associated dynamical processes settled in the natural"finite energy" space. A key point in the proof is a careful use of the energyequality, combined with the derivation of a "local compactness" estimate forsystems with supercritical nonlinearities, which may have an independentinterest. Under growth restrictions on the configuration potential, we alsoshow existence of a compact global attractor for the semiflow generated by the(weaker) solutions to the nonviscous equation characterized by a "finiteentropy" condition

Global attractors for Cahn–Hilliard equations with nonconstant mobility