Graduate School of Mathematical Sciences, The University of Tokyo
Journal of Mathematical Sciences, The University of Tokyo. Vol. 7 (2000), No. 1, Page 35-55
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.