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| Format: | Preprint |
| Veröffentlicht: |
2024
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| Online-Zugang: | https://arxiv.org/abs/2405.01038 |
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| _version_ | 1866914780948725760 |
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| author | Kolar, Miroslav Sevcovic, Daniel |
| author_facet | Kolar, Miroslav Sevcovic, Daniel |
| contents | We investigate a system of geometric evolution equations describing a curvature and torsion driven motion of a family of 3D curves in the normal and binormal directions. We explore the direct Lagrangian approach for treating the geometric flow of such interacting curves. Using the abstract theory of nonlinear analytic semi-flows, we are able to prove local existence, uniqueness, and continuation of classical Hölder smooth solutions to the governing system of non-linear parabolic equations modelling $n$ evolving curves with mutual nonlocal interactions. We present several computational studies of the flow that combine the normal or binormal velocity and considering nonlocal interaction. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_01038 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Evolution of multiple closed knotted curves in space Kolar, Miroslav Sevcovic, Daniel Analysis of PDEs Numerical Analysis Primary: 35K57, 35K65, 65N40, 65M08, Secondary: 53C80 We investigate a system of geometric evolution equations describing a curvature and torsion driven motion of a family of 3D curves in the normal and binormal directions. We explore the direct Lagrangian approach for treating the geometric flow of such interacting curves. Using the abstract theory of nonlinear analytic semi-flows, we are able to prove local existence, uniqueness, and continuation of classical Hölder smooth solutions to the governing system of non-linear parabolic equations modelling $n$ evolving curves with mutual nonlocal interactions. We present several computational studies of the flow that combine the normal or binormal velocity and considering nonlocal interaction. |
| title | Evolution of multiple closed knotted curves in space |
| topic | Analysis of PDEs Numerical Analysis Primary: 35K57, 35K65, 65N40, 65M08, Secondary: 53C80 |
| url | https://arxiv.org/abs/2405.01038 |