Abels, Helmut and Marquardt, Andreas (2021) Sharp interface limit of a Stokes/Cahn-Hilliard system Part I: Convergence result. INTERFACES AND FREE BOUNDARIES, 23 (3). pp. 353-402. ISSN 1463-9963, 1463-9971
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We consider the sharp interface limit of a coupled Stokes/Cahn-Hilliard system in a two-dimensional, bounded and smooth domain, i.e., we consider the limiting behavior of solutions when a parameter epsilon > 0 corresponding to the thickness of the diffuse interface tends to zero. We show that for sufficiently short times the solutions to the Stokes/Cahn-Hilliard system converge to solutions of a sharp interface model, where the evolution of the interface is governed by a Mullins-Sekerka system with an additional convection term coupled to a two-phase stationary Stokes system with the Young-Laplace law for the jump of an extra contribution to the stress tensor, representing capillary stresses. We prove the convergence result by estimating the difference between the exact and an approximate solutions. To this end we make use of modifications of spectral estimates shown by X. Chen for the linearized Cahn-Hilliard operator. The treatment of the coupling terms requires careful estimates, the use of the refinements of the latter spectral estimate and a suitable structure of the approximate solutions, which will be constructed in the second part of this contribution.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | CAHN-HILLIARD; EQUATIONS; EVOLUTION; Two-phase flow; diffuse interface model; sharp interface limit; Cahn-Hilliard equation; free boundary problems |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics > Prof. Dr. Helmut Abels |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 12 Jul 2022 08:19 |
| Last Modified: | 12 Jul 2022 08:19 |
| URI: | https://pred.uni-regensburg.de/id/eprint/45726 |
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