Abels, Helmut and Liu, Yuning (2018) Sharp Interface Limit for a Stokes/Allen-Cahn System. ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 229 (1). pp. 417-502. ISSN 0003-9527, 1432-0673
Full text not available from this repository. (Request a copy)Abstract
We consider the sharp interface limit of a coupled Stokes/Allen-Cahn system, when a parameter that is proportional to the thickness of the diffuse interface tends to zero, in a two dimensional bounded domain. For sufficiently small times we prove convergence of the solutions of the Stokes/Allen-Cahn system to solutions of a sharp interface model, where the interface evolution is given by the mean curvature equation with an additional convection term coupled to a two-phase Stokes system with an additional contribution to the stress tensor, which describes the capillary stress. To this end we construct a suitable approximation of the solution of the Stokes/Allen-Cahn system, using three levels of the terms in the formally matched asymptotic calculations, and estimate the difference with the aid of a suitable refinement of a spectral estimate of the linearized Allen-Cahn operator. Moreover, a careful treatment of the coupling terms is needed.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | MEAN-CURVATURE FLOW; H-INFINITY-CALCULUS; PHASE FIELD MODEL; 2-PHASE FLOWS; INCOMPRESSIBLE FLUIDS; GENERALIZED SOLUTIONS; QUALITATIVE BEHAVIOR; HILLIARD EQUATION; CLOSED OPERATORS; SURFACE-TENSION; |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics > Prof. Dr. Helmut Abels |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 09 Mar 2020 09:03 |
| Last Modified: | 09 Mar 2020 09:03 |
| URI: | https://pred.uni-regensburg.de/id/eprint/14374 |
Actions (login required)
 |
View Item |
