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arXiv · 2409.01045

A charged liquid drop model with Willmore energy

Michael Goldman·Matteo Novaga·Berardo Ruffini
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Abstract

We consider a variational model of electrified liquid drops, involving competition between surface tension and charge repulsion. Since the natural model happens to be ill-posed, we show that by adding to the perimeter a Willmore-type energy, the problem turns back to be well-posed. We also prove that for small charge the droplets is spherical.

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Michael Goldman, Matteo Novaga, Berardo Ruffini. 2024-09-02. A charged liquid drop model with Willmore energy. https://arxiv.org/abs/2409.01045

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