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CNA Seminar/Colloquium/Joint Pitt-CNA Colloquium

Zoran Grujic
University of Virginia
Title: Turbulent cascades and regularity theory in physical scales of 3D incompressible fluid flows

Abstract: A mathematical framework for the study of turbulent cascades in physical scales of 3D incompressible fluid flows has been recently introduced in a joint work with R. Dascaliuc. The main idea was to first `discretize' the flow by localizing it to a suitable family of balls at a given scale, and then to `reconstruct' it via an ensemble-averaging process capable of detecting significant sign-fluctuations of a physical density at the given scale (for example, in the case of the energy cascade, the a priori sign-varying density of interest is the energy flux).

The goal of this lecture is to show how this general framework leads to a proof of existence and scale-locality of the anisotropic 3D enstrophy cascade (enstrophy being the $L^2$-norm of the vorticity), as well as to indicate how the aforementioned ensemble-averaging process can be utilized -- in conjunction with a newly-discovered geometric measure-type regularity criterion -- to indicate a geometric scenario leading to closing the scaling gap in the regularity problem for the 3D Navier-Stokes equations.

Pdf File: GrujicZoran.pdf
Date: Tuesday, January 24, 2012
Time: 1:30 pm
Location: Wean Hall 7218
Submitted by:  Gautam Iyer