Abels, Helmut and Fei, Mingwen and Moser, Maximilian (2024) Sharp interface limit for a Navier-Stokes/Allen-Cahn system in the case of a vanishing mobility. CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 63 (4): 94. ISSN 0944-2669, 1432-0835
Full text not available from this repository. (Request a copy)Abstract
We consider the sharp interface limit of a Navier-Stokes/Allen Cahn equation in a bounded smooth domain in two space dimensions, in the case of vanishing mobility m(epsilon)=root epsilon, where the small parameter epsilon>0 related to the thickness of the diffuse interface is sent to zero. For well-prepared initial data and sufficiently small times, we rigorously prove convergence to the classical two-phase Navier-Stokes system with surface tension. The idea of the proof is to use asymptotic expansions to construct an approximate solution and to estimate the difference of the exact and approximate solutions with a spectral estimate for the (at the approximate solution) linearized Allen-Cahn operator. In the calculations we use a fractional order ansatz and new ansatz terms in higher orders leading to a suitable epsilon-scaled and coupled model problem. Moreover, we apply the novel idea of introducing epsilon-dependent coordinates.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | FRONT PROPAGATION PROBLEMS; ALLEN-CAHN; MEAN-CURVATURE; GENERALIZED MOTION; CONVERGENCE-RATES; EQUATION; HILLIARD; FLOWS; MODEL; Primary: 76T99; Secondary: 35Q30; 35Q35; 35R35; 76D05; 76D45 |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics > Prof. Dr. Helmut Abels |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 26 Aug 2025 09:49 |
| Last Modified: | 26 Aug 2025 09:49 |
| URI: | https://pred.uni-regensburg.de/id/eprint/64056 |
Actions (login required)
 |
View Item |
