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**Stokes problems for moving half-planes.**
*(English)*
Zbl 0843.76015

New exact solutions of Navier-Stokes equations describing the impulsive and oscillatory driven flows in a half-space or in a channel are presented. These solutions have a two-dimensional structure in the region near to the contact between the half-infinite plates. The exact fundamental solutions are also obtained for the flow in a half-space driven by the tangential edgewise motion of half-infinite plate. These solutions are then used to find the solutions for the channel flows which can be obtained by adding an infinite series solution derived from a reflection procedure, by using the fact that the non-slip boundary condition is satisfied on the top wall.

Reviewer: R.Stavre (Bucureşti)

### MSC:

76D05 | Navier-Stokes equations for incompressible viscous fluids |

### Keywords:

oscillatory and impulsive motions; superposition technique; exact solutions; channel; infinite series solution; reflection procedure
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\textit{Y. Zeng} and \textit{S. Weinbaum}, J. Fluid Mech. 287, 59--74 (1995; Zbl 0843.76015)

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DOI

### References:

[1] | DOI: 10.1016/0021-9290(94)90010-8 |

[2] | Stokes, Trans. Camb. Phil. Soc. 9 pp 8– (1851) |

[3] | Kerczek, J. Fluid Mech. 62 pp 753– (1974) |

[4] | Hall, J. Fluid Mech. 146 pp 347– (1984) |

[5] | Dewey, Trans. ASME 103 pp 177– (1981) |

[6] | DOI: 10.1146/annurev.fl.08.010176.000421 |

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