Topological methods in hydrodynamics

  title={Topological methods in hydrodynamics},
  author={Vladimir I. Arnold and Boris A. Khesin},
A group theoretical approach to hydrodynamics considers hydrodynamics to be the differential geometry of diffeomorphism groups. The principle of least action implies that the motion of a fluid is described by the geodesics on the group in the right-invariant Riemannian metric given by the kinetic energy. Investigation of the geometry and structure of such groups turns out to be useful for describing the global behavior of fluids for large time intervals. 

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