## Abstract

Hilbert formulas for an r-analytic function, defined by a generalized Cauchy-Riemann system in the domain exterior to the contour of a spindle in the meridional cross-section plane, have been derived. The derivation is based on the theory of Riemann boundary-value problems for analytic functions. For numerical calculations, Fourier integrals with Hilbert formulas representing the real and imaginary parts of the r-analytic function have been reduced to the form of regular integrals. The problem of the axially symmetric steady motion of a rigid spindle-shaped body in a Stokes fluid has been solved, and the pressure in the fluid has been expressed analytically based on a Hilbert formula. As an illustration, streamlines about the body, vortex and pressure functions at the contour of the body, and the drag force, exerted on the body by the fluid, have been calculated.

Original language | English |
---|---|

Pages (from-to) | 1270-1300 |

Number of pages | 31 |

Journal | SIAM Journal on Applied Mathematics |

Volume | 66 |

Issue number | 4 |

DOIs | |

State | Published - 2006 |

## ASJC Scopus subject areas

- Applied Mathematics

## Keywords

- Analytic function
- Bipolar coordinates
- Drag force
- Fourier integral transform
- Hubert formula
- Lame equation
- Pressure
- Riemann boundary-value problem
- Spindle
- Stokes equations
- Vorticity
- r-analytic function