Mathematical Foundation of Turbulent Viscous Flows

Volume 1871 of the series Lecture Notes in Mathematics pp 1-43


Euler Equations, Navier-Stokes Equations and Turbulence

  • Peter ConstantinAffiliated withDepartment of Mathematics, University of Chicago

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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]).