On the topology of three-dimensional steady flows of an ideal fluid

  • Vladimir I. Arnold
Part of the Vladimir I. Arnold - Collected Works book series (ARNOLD, volume 2)


We shall consider the rotational steady flows of an incompressible inviscid fluid in a bounded region D. It will be assumed that the vectors of velocity and vorticity are not everywhere colinear. It will be shown that the region of flow D is divided by the critical ’Bernoulli surfaces’ into a finite number of cells, in each of which the streamlines are either closed, or else, everywhere they closely encircle toroidal surfaces.


Mathematical Application Mathematical Method Finite Number Algebraic Geometry Steady Flow 
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Copyright information

© Nauka, Moscow 1966

Authors and Affiliations

  • Vladimir I. Arnold
    • 1
  1. 1.HeidelbergGermany

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