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arXiv · 1212.3625

Dynamic Stability of Equilibrium Capillary Drops

William M. Feldman·Inwon C. Kim
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Abstract

We investigate a model for contact angle motion of quasi-static capillary drops resting on a horizontal plane. We prove global in time existence and long time behavior (convergence to equilibrium) in a class of star-shaped initial data for which we show that topological changes of drops can be ruled out for all times. Our result applies to any drop which is initially star-shaped with respect to a a small ball inside the drop, given that the volume of the drop is sufficiently large. For the analysis, we combine geometric arguments based on the moving-plane type method with energy dissipation methods based on the formal gradient flow structure of the problem.

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William M. Feldman, Inwon C. Kim. 2012-12-14. Dynamic Stability of Equilibrium Capillary Drops. https://doi.org/10.1007/s00205-013-0698-5

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