Garcke, Harald and Wieland, Sandra (2006) Surfactant spreading on thin viscous films: Nonnegative solutions of a coupled degenerate system. SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 37 (6). pp. 2025-2048. ISSN 0036-1410, 1095-7154
Full text not available from this repository. (Request a copy)Abstract
We consider the Navier-Stokes system for an incompressible fluid coupled with a convection-diffusion equation for surfactant molecules on the free surface. The lubrication approximation leads to a coupled system of parabolic equations, consisting of a degenerate fourth-order equation for the film height and a second-order equation for the surfactant concentration. A proof based on energy estimates shows the existence of global weak solutions which in addition fulfill an integral inequality (entropy condition) which ensures positivity properties for the solution.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | CAHN-HILLIARD EQUATION; LUBRICATION APPROXIMATION; PARABOLIC EQUATION; EXISTENCE; EVOLUTION; BEHAVIOR; partial differential equations; degenerate parabolic equation; thin liquid film; surfactant spreading; free surface; fluid interface |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics > Prof. Dr. Harald Garcke |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 03 Mar 2021 10:56 |
| Last Modified: | 03 Mar 2021 10:56 |
| URI: | https://pred.uni-regensburg.de/id/eprint/35280 |
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