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arXiv · 1109.6762

Weak solutions to a thin film model with capillary effects and insoluble surfactant

Joachim Escher·Matthieu Hillairet·Philippe Laurencot·Christoph Walker
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Abstract

The paper focuses on a model describing the spreading of an insoluble surfactant on a thin viscous film with capillary effects taken into account. The governing equation for the film height is degenerate parabolic of fourth order and coupled to a second order parabolic equation for the surfactant concentration. It is shown that nonnegative weak solutions exist under natural assumptions on the surface tension coefficient.

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Joachim Escher, Matthieu Hillairet, Philippe Laurencot, Christoph Walker. 2011-09-30. Weak solutions to a thin film model with capillary effects and insoluble surfactant. https://doi.org/10.1088/0951-7715%2F25%2F9%2F2423

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