Abels, Helmut and Garcke, Harald and Poiatti, Andrea (2025) Diffuse interface model for two-phase flows on evolving surfaces with different densities: global well-posedness. CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 64 (5): 141. ISSN 0944-2669, 1432-0835
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We show global in time existence and uniqueness on any finite time interval of strong solutions to a Navier-Stokes/Cahn-Hilliard type system on a given two-dimensional evolving surface in the case of different densities and a singular (logarithmic) potential. The system describes a diffuse interface model for a two-phase flow of viscous incompressible fluids on an evolving surface. We also establish the validity of the instantaneous strict separation property from the pure phases. To show these results we use our previous achievements on local well-posedness together with suitable novel regularity results for the convective Cahn-Hilliard equation. The latter allows to obtain higher-order energy estimates to extend the local solution globally in time. To this aim the time evolution of energy type quantities has to be calculated and estimated carefully.
| Item Type: | Article |
|---|---|
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics > Prof. Dr. Helmut Abels Mathematics > Prof. Dr. Harald Garcke |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 05 May 2026 05:55 |
| Last Modified: | 05 May 2026 05:55 |
| URI: | https://pred.uni-regensburg.de/id/eprint/66819 |
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