# Analysis & Applied Math

Event Information Enstropy growth and the Navier-Stokes Strain Equation
13:10 on Friday November 17, 2017
14:00 on Friday November 17, 2017
BA6183, Bahen Center, 40 St. George St.
Evan Miller

University of Toronto

We prove the existence of mild solutions in $L^2$ to the evolution equation governing the symmetric part of the gradient (the strain tensor) in the incompressible Navier Stokes equation in $R^3$.We will use this PDE to derive a simplified identity for the growth of enstrophy $E(t)$ for mild solutions that depends only on the strain tensor, not on the interaction of the strain tensor with the vorticity; this will also allow an improvement of the constant in the differential inequality for enstrophy growth of the form $E' \le C E^3$ by a factor of nearly half a million. We will use this to provide a lower bound on blow-up time in terms of the initial enstrophy, as well as provide analytical evidence for the observed alignment of vorticity to the middle eigenvector of the strain matrix. Finally, we will prove some properties about blowup for a toy model ODE of the strain tensor evolution equation.