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

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arxiv 2006.04994 v2 pith:422DDB6X submitted 2020-06-09 math.AP physics.flu-dyn

Hangjie Ji , Roman Taranets , Marina Chugunova This is my paper · ORCID
classification math.APphysics.flu-dyn
keywords modelsolutionstravellingdownfibrefilmflowingliquid
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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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