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TURW02 - Rigorous analysis of incompressible fluid models and turbulence

Taking account of the intermittency effect, we introduce the notion of determining wavenumber for a turbulent vector field without any assumption on the regularity. The time average of the determining wavenumber is shown to be bounded by Kolmogorov’s dissipation wavenumber $K_d$. It provides a rigorous justification of Kolmogorov’s prediction that the wavenumber $K_d$ separates the inertial range from the dissipation range. Inspirations for the regularity theory of the Navier-Stokes equation will be also discussed.  

This talk is part of the Isaac Newton Institute Seminar Series series.

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