Abels, Helmut and Weber, Josef (2020) Local well-posedness of a quasi-incompressible two-phase flow. JOURNAL OF EVOLUTION EQUATIONS. ISSN 1424-3199, 1424-3202
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We show well-posedness of a diffuse interface model for a two-phase flow of two viscous incompressible fluids with different densities locally in time. The model leads to an inhomogeneous Navier-Stokes/Cahn-Hilliard system with a solenoidal velocity field for the mixture, but a variable density of the fluid mixture in the Navier-Stokes type equation. We prove existence of strong solutions locally in time with the aid of a suitable linearization and a contraction mapping argument. To this end, we show maximal L-2-regularity for the Stokes part of the linearized system and use maximal L-p-regularity for the linearized Cahn-Hilliard system.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | DIFFUSE INTERFACE MODEL; WEAK SOLUTIONS; EXISTENCE; FLUIDS; Two-phase flow; Navier-Stokes equation; Diffuse interface model; Mixtures of viscous fluids; Cahn-Hilliard equation |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics > Prof. Dr. Helmut Abels |
| Depositing User: | Petra Gürster |
| Date Deposited: | 21 Apr 2021 07:25 |
| Last Modified: | 21 Apr 2021 07:25 |
| URI: | https://pred.uni-regensburg.de/id/eprint/43384 |
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