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Convergence of a nonlocal to a local diffuse interface model for two-phase flow with unmatched densities

  • * Corresponding author: Helmut Abels

    * Corresponding author: Helmut Abels 

The second author has been supported by JSPS KAKENHI number 17K17804

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  • We prove convergence of suitable subsequences of weak solutions of a diffuse interface model for the two-phase flow of incompressible fluids with different densities with a nonlocal Cahn-Hilliard equation to weak solutions of the corresponding system with a standard "local" Cahn-Hilliard equation. The analysis is done in the case of a sufficiently smooth bounded domain with no-slip boundary condition for the velocity and Neumann boundary conditions for the Cahn-Hilliard equation. The proof is based on the corresponding result in the case of a single Cahn-Hilliard equation and compactness arguments used in the proof of existence of weak solutions for the diffuse interface model.

    Mathematics Subject Classification: Primary: 76T99; Secondary: 35Q30, 35Q35, 76D03, 76D05, 76D27, 76D45.

    Citation:

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