Abels, Helmut (2012) STRONG WELL-POSEDNESS OF A DIFFUSE INTERFACE MODEL FOR A VISCOUS, QUASI-INCOMPRESSIBLE TWO-PHASE FLOW. SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 44 (1). pp. 316-340. ISSN 0036-1410,
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In this article we discuss the existence of strong solutions locally in time for a model of a binary mixture of viscous incompressible fluids in a bounded domain. The model was derived by Lowengrub and Truskinovski. It is used to describe a diffuse interface model for a two-phase flow of two viscous incompressible Newtonian fluids with different densities. The fluids are macroscopically immiscible but partially mix in a small interfacial region. The model leads to a system of Navier-Stokes/Cahn-Hilliard type. Using a suitable result on maximal L-2-regularity for the linearized system, the existence of strong solutions is shown with the aid of the contraction mapping principle. The analysis shows that in the case of different densities the system is coupled in highest order and the principal part of the linearized system is of very different structure compared to the case of same densities. The linear system is solved with the aid of a general result on an abstract damped wave equation by Chen and Triggiani.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | CAHN-HILLIARD FLUIDS; PHASE-FIELD MODEL; HELE-SHAW CELL; ORDER-PARAMETER; SPACES; RECONNECTION; PINCHOFF; MIXTURE; BESOV; two-phase flow; free boundary value problems; diffuse interface model; mixtures of viscous fluids; Cahn-Hilliard equation; inhomogeneous Navier-Stokes equation |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics > Prof. Dr. Helmut Abels |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 25 May 2020 07:52 |
| Last Modified: | 25 May 2020 07:52 |
| URI: | https://pred.uni-regensburg.de/id/eprint/19537 |
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