The Cahn-Hilliard system has been introduced in material science to describe at a macroscopic level the formation and evolution of microstructures during the phase segregation in a binary alloys system. This phenomenon occurs when a homogeneous mixture undergoes a rapid cooling below a critical temperature. More recently, a nonlocal version of the Cahn-Hilliard system has been proposed by Giacomin and Lebowitz. This macroscopic equation has been rigorously derived starting from a microscopic formulation and taking into account long range repulsive interactions between different species and short hard collisions between all particles. The resulting model is a conserved gradient flow associated to the so called nonlocal Helmholtz free energy. During the talk we will discuss some recent results concerning the nonlocal Cahn-Hilliard system in the case of thermodynamically relevant logarithmic potentials. More precisely, we will show the long-time regularity of weak solutions and the validity of the separation property.

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