Tohoku Mathematical Journal
2003
June
SECOND SERIES VOL. 55, NO. 2

Tohoku Math. J.
55 (2003), 311-320

Title VORTEX FILAMENT EQUATION IN A RIEMANNIAN MANIFOLD

Author Norihito Koiso

(Received May 28, 2001, revised July 23, 2002)
Abstract. We define a Riemannian version of the vortex filament equation. Using perturbation to a parabolic equation, we prove the short time unique existence of a solution for any initial closed curve.

2000 Mathematics Subject Classification. Primary 53C44; Secondary 35Q35, 35B25.
Key words and phrases. Vortex filament, Riemannian manifold, singular perturbation.

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