Center for                           Nonlinear Analysis CNA Home People Seminars Publications Workshops and Conferences CNA Working Groups CNA Comments Form Summer Schools Summer Undergraduate Institute PIRE Cooperation Graduate Topics Courses SIAM Chapter Seminar Positions Contact 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.pdfDate: Tuesday, January 24, 2012Time: 1:30 pmLocation: Wean Hall 7218Submitted by:  Gautam Iyer