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arXiv · 2006.04994

On travelling wave solutions of a model of a liquid film flowing down a fibre

Hangjie Ji·Roman Taranets·Marina Chugunova
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Abstract

Existence of non-negative weak solutions is shown for a full curvature thin-film model of a liquid thin film flowing down a vertical fibre. The proof is based on the application of a priori estimates derived for energy-entropy functionals. Long-time behaviour of these weak solutions is analysed and, under some additional constraints for the model parameters and initial values, convergence towards a travelling wave solution is obtained. Numerical studies of energy minimizers and travelling waves are presented to illustrate analytical results.

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Hangjie Ji, Roman Taranets, Marina Chugunova. 2020-06-09. On travelling wave solutions of a model of a liquid film flowing down a fibre. https://arxiv.org/abs/2006.04994

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