Abels, Helmut and Fischer, Julian and Moser, Maximilian (2024) Approximation of Classical Two-Phase Flows of Viscous Incompressible Fluids by a Navier-Stokes/Allen-Cahn System. ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 248 (5): 77. ISSN 0003-9527, 1432-0673
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We show convergence of the Navier-Stokes/Allen-Cahn system to a classical sharp interface model for the two-phase flow of two viscous incompressible fluids with same viscosities in a smooth bounded domain in two and three space dimensions as long as a smooth solution of the limit system exists. Moreover, we obtain error estimates with the aid of a relative entropy method. Our results hold provided that the mobility m(epsilon)>0 in the Allen-Cahn equation tends to zero in a subcritical way, i.e., m(epsilon)=m(0)epsilon(beta) for some beta is an element of (0,2) and m(0)>0. The proof proceeds by showing via a relative entropy argument that the solution to the Navier-Stokes/Allen-Cahn system remains close to the solution of a perturbed version of the two-phase flow problem, augmented by an extra mean curvature flow term m(epsilon)H(Gamma t )in the interface motion. In a second step, it is easy to see that the solution to the perturbed problem is close to the original two-phase flow.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | SHARP INTERFACE LIMIT; CONVERGENCE-RATES; CURVATURE FLOW; EQUATIONS; BEHAVIOR; MODEL; Primary: 76T06; Secondary: 35Q30; 35Q35; 35R35; 76D05; 76D45 |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics Mathematics > Prof. Dr. Helmut Abels |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 25 Jul 2025 08:13 |
| Last Modified: | 25 Jul 2025 08:13 |
| URI: | https://pred.uni-regensburg.de/id/eprint/63756 |
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