A charged liquid drop model with Willmore energy
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866917777598578688 |
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| author | Goldman, Michael Novaga, Matteo Ruffini, Berardo |
| author_facet | Goldman, Michael Novaga, Matteo Ruffini, Berardo |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_01045 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A charged liquid drop model with Willmore energy Goldman, Michael Novaga, Matteo Ruffini, Berardo Analysis of PDEs 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. |
| title | A charged liquid drop model with Willmore energy |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2409.01045 |