Attractors for a Navier–Stokes–Allen–Cahn system with unmatched densities

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Abstract

This paper investigates the long-time behavior for a Navier–Stokes–Allen–Cahn system, a diffuse interface model for two-phase incompressible flows with unmatched densities, non-constant viscosities, and a singular Flory–Huggins potential. First, we establish the dissipativity of strong solutions via some a priori estimates. Then, we demonstrate the regular-continuity of the semigroup, which allows us to prove the existence of the global attractor in the strong solutions space.

Keywords

two phase flow / global attractor / Navier–Stokes–Allen–Cahn system / dissipativity / singular Flory–Huggins potential

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