Nonlinear Partial Differential Equations

Date: November 23, 2021

Time: 3:00PM - 4:00PM

Location: Zoom

Speaker: Aseel Farhat, Florida State University

Title: Intermittency in turbulence and the 3D Navier-Stokes regularity problem

Abstract: We describe several aspects of an analytic/geometric framework for the three-dimensional Navier-Stokes regularity problem, which is directly inspired by the morphology of the regions of intense vorticity/velocity gradients observed in computational simulations of three-dimensional turbulence. Among these, we present our proof that the scaling gap in the 3D Navier-Stokes regularity problem can be reduced by an algebraic factor within an appropriate functional setting incorporating the intermittency of the spatial regions of high vorticity. Furthermore, a turbulent cascade model based on the suitably defined scale of sparseness of the super-level sets of the higher-order derivatives of the velocity field is examined. In particular, a certain universality property of the ratios of the scales of sparseness at nearby (differential) levels is discovered.