JournalsprimsVol. 33, No. 4pp. 509–526

Solvability of Equations for Motion of a Vortex Filament with or without Axial Flow

  • Atusi Tani

    Tokyo Institute of Technology, Japan
  • Takahiro Nishiyama

    Keio University, Yokohama, Japan
Solvability of Equations for Motion of a Vortex Filament with or without Axial Flow cover
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Abstract

It is known that the motion of a vortex filament with axial flow in a perfect fluid is approximately described by a generalization of the localized induction equation. The unique solvability of the initial value problem for it is first established by parabolic regularization. As the axial flow effect vanishes, its solution converges to that of the localized induction equation. Analogous results are obtained in the spatially periodic case.

Cite this article

Atusi Tani, Takahiro Nishiyama, Solvability of Equations for Motion of a Vortex Filament with or without Axial Flow. Publ. Res. Inst. Math. Sci. 33 (1997), no. 4, pp. 509–526

DOI 10.2977/PRIMS/1195145146