Euler Equations, Navier-Stokes Equations and Turbulence

  • Peter Constantin
Chapter
Part of the Lecture Notes in Mathematics book series (LNM, volume 1871)

Abstract

In 2004 the mathematical world will mark 120 years since the advent of turbulence theory ([80]). In his 1884 paper Reynolds introduced the decomposition of turbulent flow into mean and fluctuation and derived the equations that describe the interaction between them. The Reynolds equations are still a riddle. They are based on the Navier-Stokes equations, which are a still a mystery. The Navier-Stokes equations are a viscous regularization of the Euler equations, which are still an enigma. Turbulence is a riddle wrapped in a mystery inside an enigma ([11]).

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Copyright information

© Springer-Verlag Berlin/Heidelberg 2006

Authors and Affiliations

  • Peter Constantin
    • 1
  1. 1.Department of MathematicsUniversity of ChicagoU.S.A.

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