Y. Charles Li
Published 2005-07-13Version 1
In this article, I would like to express some of my views on the nature of turbulence. These views are mainly drawn from the author's recent results on chaos in partial differential equations \cite{Li04}. Fluid dynamicists believe that Navier-Stokes equations accurately describe turbulence. A mathematical proof on the global regularity of the solutions to the Navier-Stokes equations is a very challenging problem. Such a proof or disproof does not solve the problem of turbulence. It may help understanding turbulence. Turbulence is more of a dynamical system problem. Studies on chaos in partial differential equations indicate that turbulence can have Bernoulli shift dynamics which results in the wandering of a turbulent solution in a fat domain in the phase space. Thus, turbulence can not be averaged. The hope is that turbulence can be controlled.
Chaos in Partial Differential Equations, Navier-Stokes Equations and Turbulence
Kolmogorov's Theory of Turbulence and Inviscid Limit of the Navier-Stokes Equations in $\R^3$
Remarks on a quasi-linear model of the Navier-Stokes Equations
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