Global weak solutions and exponential decay to the flat equilibrium are shown for the full thin film surfactant system with gravity, capillary, and van der Waals forces under explicit smallness conditions in Wiener algebras.
On an asymptotic model for free boundary Darcy flow in porous media
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abstract
We provide a rigorous mathematical study of an asymptotic model describing Darcy flow with free boundary in a low amplitude/large wavelength approximation. In particular, we prove several well-posedness results in critical spaces. Furthermore, we also study how the solution decays towards the flat equilibrium.
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On a thin film model with insoluble surfactant
Global weak solutions and exponential decay to the flat equilibrium are shown for the full thin film surfactant system with gravity, capillary, and van der Waals forces under explicit smallness conditions in Wiener algebras.