Existence of a Solution to the Mixed Problem for a Vortex Filament Equation with an External Flow Term

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Existence of a Solution to the Mixed Problem for a Vortex Filament Equation with an External Flow Term

J. Math. Sci. Univ. Tokyo
Vol. 7 (2000), No. 1, Page 35--55.

Nishiyama, Takahiro
Existence of a Solution to the Mixed Problem for a Vortex Filament Equation with an External Flow Term
[Full Article (PDF)] [MathSciNet Review (HTML)] [MathSciNet Review (PDF)]

Abstract:
The three-dimensional motion of a segment of a vortex filament embedded in an external flow is considered under the localized induction approximation. The mixed problem for a vector equation which describes this motion is proved to have at least one solution by using the parabolic regularization method of the second order.

Mathematics Subject Classification (1991): Primary 35Q35, 76C05, 76Y05; Secondary 35K55

Mathematical Reviews Number: MR1749980

Received: 1998-07-27

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