We prove convergence of a sequence of strong solutions to a diffuse interface model for the two-phase flow of incompressible fluids with matched densities with a nonlocal Cahn-Hilliard equation to the strong solution to the corresponding system with a standard local Cahn-Hilliard equation. The analysis is done in the case of constant viscosity. The proof is based on an energy method and convergence of the linearized operators in the Cahn-Hilliard equations. > References > [1] H. Abels, C. Hurm. Strong nonlocal-to-local convergence of the Cahn-Hilliard equation and its operator. J. Differential Equations, 402: 593-624, 2024. > [2] C. Hurm, P. Knopf, A. Poiatti. Nonlocal-to-local convergence rates for strong solutions to a Navier-Stokes-Cahn-Hilliard system with singular potential. Communications in Partial Differential Equations, 49(9), 832-871, 2024.
