On travelling wave solutions of a model of a liquid film flowing down a fibre
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.
- Publication:
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arXiv e-prints
- Pub Date:
- June 2020
- DOI:
- 10.48550/arXiv.2006.04994
- arXiv:
- arXiv:2006.04994
- Bibcode:
- 2020arXiv200604994J
- Keywords:
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- Mathematics - Analysis of PDEs;
- Physics - Fluid Dynamics
- E-Print:
- 30 pages, 6 figures