Existence of flat flows for volume-preserving mean curvature flow with contact angle
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866915509822291968 |
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| author | Jang, Jiwoong |
| author_facet | Jang, Jiwoong |
| contents | We study the motion of a droplet evolving by mean curvature with volume constraint and contact angle condition on a half space. We prove the existence of a global-in-time weak solution, called the flat flow. A difficulty arises when we establish the local-in-time equi-boundedness of approximate solutions and a uniform $L^2$-estimate of multipliers. The difficulty is handled by conducting blowup analysis at a point in contact to a spherical cap with sharp angle. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_19470 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Existence of flat flows for volume-preserving mean curvature flow with contact angle Jang, Jiwoong Analysis of PDEs 35D30, 49J53, 53E10, 58E12 We study the motion of a droplet evolving by mean curvature with volume constraint and contact angle condition on a half space. We prove the existence of a global-in-time weak solution, called the flat flow. A difficulty arises when we establish the local-in-time equi-boundedness of approximate solutions and a uniform $L^2$-estimate of multipliers. The difficulty is handled by conducting blowup analysis at a point in contact to a spherical cap with sharp angle. |
| title | Existence of flat flows for volume-preserving mean curvature flow with contact angle |
| topic | Analysis of PDEs 35D30, 49J53, 53E10, 58E12 |
| url | https://arxiv.org/abs/2509.19470 |