Abels, Helmut and Terasawa, Yutaka (2022) CONVERGENCE OF A NONLOCAL TO A LOCAL DIFFUSE INTERFACE MODEL FOR TWO-PHASE FLOW WITH UNMATCHED DENSITIES. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES S, 15 (8). pp. 1871-1881. ISSN 1937-1632, 1937-1179
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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.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | CAHN-HILLIARD EQUATION; INCOMPRESSIBLE FLUIDS; WEAK SOLUTIONS; EXISTENCE; Two-phase flow; Navier-Stokes equation; diffuse interface model; mix-tures of viscous fluids; Cahn-Hilliard equation; non-local operators |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics > Prof. Dr. Helmut Abels |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 07 Feb 2024 09:30 |
| Last Modified: | 07 Feb 2024 09:30 |
| URI: | https://pred.uni-regensburg.de/id/eprint/56978 |
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