Abels, Helmut and Fei, Mingwen (2023) SHARP INTERFACE LIMIT FOR A NAVIER--STOKES/ALLEN--CAHN SYSTEM WITH DIFFERENT VISCOSITIES. SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 55 (4). pp. 4039-4088. ISSN 0036-1410, 1095-7154
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We discuss the sharp interface limit of a coupled Navier--Stokes/Allen--Cahn system in a two dimensional, bounded and smooth domain, when a parameter epsilon > 0 that is proportional to the thickness of the diffuse interface tends to zero, rigorously. We prove convergence of the solutions of the Navier--Stokes/Allen--Cahn system to solutions of a sharp interface model, where the interface evolution is given by the mean curvature flow with an additional convection term coupled to a two-phase Navier-Stokes system with surface tension. This is done by constructing an approximate solution from the limiting system via matched asymptotic expansions together with a novel ansatz for the highest order term, and then estimating its difference with the real solution with the aid of a refined spectral estimate of the linearized Allen--Cahn operator near the approximate solution.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | MEAN-CURVATURE FLOW; WELL-POSEDNESS; GENERALIZED MOTION; BOUNDARY-CONDITION; CONVERGENCE; EQUATION; MODEL; BEHAVIOR; FLUIDS; ANGLE; two-phase flow; diffuse interface model; sharp interface limit; Allen--Cahn equation; Navier-Stokes equation |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics Mathematics > Prof. Dr. Helmut Abels |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 19 Apr 2024 15:13 |
| Last Modified: | 19 Apr 2024 15:13 |
| URI: | https://pred.uni-regensburg.de/id/eprint/61573 |
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