Long time existence for vortex filament equation in a Riemannian manifold
Vortex filament equation in the Euclidean space has a long time solution for any closed initial data, because it can be converted into a standard nonlinear Schrödinger equation. While the Riemannian version of vortex filament equation is not integrable at all, we prove that it has a long time soluti...
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| Veröffentlicht in: | Osaka journal of mathematics 2008-06, Vol.45 (no. 2), p.265-271 |
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| Format: | Artikel |
| Sprache: | eng |
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| Online-Zugang: | Volltext |
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| Zusammenfassung: | Vortex filament equation in the Euclidean space has a long
time solution for any closed initial data, because it can
be converted into a standard nonlinear Schrödinger
equation. While the Riemannian version of vortex filament
equation is not integrable at all, we prove that it has a
long time solution for any closed initial data. |
|---|