Steady Oseen Flow in Exterior Domains

  • Giovanni P. Galdi
Part of the Springer Tracts in Natural Philosophy book series (STPHI, volume 38)


As we observed in the Introduction to Chapter V, the Stokes approximation fails to describe the physical properties of a system constituted by an object B moving with a small, constant velocity in a viscous liquid, at least at large distances from B where the viscous effects become less important. In particular, for B a ball, the explicit solution one finds (see (V.0.3)) exhibits no wake behind the body and is, therefore, unacceptable from the physical viewpoint. Moreover, for B a circle (plane motion), the problem admits no solution except for the trivial one. In addition to this, as observed by Oseen (1927, p.165), for the solution (V.0.3) we obtain, after a simple calculation,
$$ \left| {\frac{{{\text{v}} \cdot \nabla {\text{v}}}}{{\Delta {\text{v}}}}} \right| \to \infty {\kern 1pt} {\text{as}}\left| x \right| \to \infty , $$
no matter how small v is, thus violating the assumption under which the Stokes equations are derived (see the Introduction to Chapter IV).


Fundamental Solution Pressure Field Stokes Problem Exterior Domain Stokes System 
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Copyright information

© Springer Science+Business Media New York 1994

Authors and Affiliations

  • Giovanni P. Galdi
    • 1
  1. 1.Istituto di IngegneriaUniversità di FerraraFerraraItaly

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