Mathematical Foundation of Turbulent Viscous Flows pp 1-43

Part of the Lecture Notes in Mathematics book series (LNM, volume 1871)

Euler Equations, Navier-Stokes Equations and Turbulence

  • Peter Constantin
Chapter

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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