Abels, Helmut and Marquardt, Andreas (2021) Sharp Interface Limit of a Stokes/Cahn-Hilliard System, Part II: Approximate Solutions. JOURNAL OF MATHEMATICAL FLUID MECHANICS, 23 (2): 38. ISSN 1422-6928, 1422-6952
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We construct rigorously suitable approximate solutions to the Stokes/Cahn-Hilliard system by using the method of matched asymptotics expansions. This is a main step in the proof of convergence given in the first part of this contribution, [3], where the rigorous sharp interface limit of a coupled Stokes/Cahn-Hilliard system in a two dimensional, bounded and smooth domain is shown. As a novelty compared to earlier works, we introduce fractional order terms, which are of significant importance, but share the problematic feature that they may not he uniformly estimated in e in arbitrarily strong norms. As a consequence, gaining necessary estimates for the error, which occurs when considering the approximations in the Stokes/Cahn-Hilliard system, is rather involved.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | 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: | 06 Jul 2022 06:21 |
| Last Modified: | 06 Jul 2022 06:21 |
| URI: | https://pred.uni-regensburg.de/id/eprint/45736 |
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