On the Cauchy problem for a dynamical Euler's elastica
| dc.creator | Burchard, Almut | |
| dc.creator | Thomas, Lawrence E. | |
| dc.date | 2002-02-26 | |
| dc.date | 2002-06-11 | |
| dc.date.accessioned | 2026-07-07T04:46:42Z | |
| dc.date.available | 2026-07-07T04:46:42Z | |
| dc.description | The dynamics for a thin, closed loop inextensible Euler's elastica moving in three dimensions are considered. The equations of motion for the elastica include a wave equation involving fourth order spatial derivatives and a second order elliptic equation for its tension. A Hasimoto transformation is used to rewrite the equations in convenient coordinates for the space and time derivatives of the tangent vector. A feature of this elastica is that it exhibits time-dependent monodromy. A frame parallel-transported along the elastica is in general only quasi-periodic, resulting in time-dependent boundary conditions for the coordinates. This complication is addressed by a gauge transformation, after which a contraction mapping argument can be applied. Local existence and uniqueness of elastica solutions are established for initial data in suitable Sobolev spaces. | |
| dc.description | 31 pages. Revised introduction | |
| dc.identifier | https://arxiv.org/abs/math/0202278 | |
| dc.identifier | http://arxiv.org/abs/math/0202278 | |
| dc.identifier | Communications in PDE 28 (2003), 271-300 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/63440 | |
| dc.subject | Analysis of PDEs | |
| dc.subject | Mathematical Physics | |
| dc.subject | 35Q72 (74K10) | |
| dc.title | On the Cauchy problem for a dynamical Euler's elastica | |
| dc.type | text |