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Euler Equations, Navier-Stokes Equations and Turbulence

Part of the Lecture Notes in Mathematics book series (LNMCIME,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]).

Keywords

  • Weak Solution
  • Euler Equation
  • Besov Space
  • Vortex Line
  • Energy Dissipation Rate

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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© 2006 Springer-Verlag Berlin/Heidelberg

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Constantin, P. (2006). Euler Equations, Navier-Stokes Equations and Turbulence. In: Cannone, M., Miyakawa, T. (eds) Mathematical Foundation of Turbulent Viscous Flows. Lecture Notes in Mathematics, vol 1871. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11545989_1

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