## Graduate Analysis Seminar

Trevor Leslie

The Energy Measure for the Navier-Stokes Equations

**Abstract:**The potential failure of energy equality for a solution $u$ of the Euler or Navier-Stokes Equations (NSE) can be quantified using a so-called `energy measure': the weak-$*$ limit of the measures $|u(t)|^2\,dx$ as $t$ approaches the first possible blowup time. Focusing on the case of the 3-dimensional NSE, we discuss reasons why the energy measure is an object worthy of study and prove some of its basic measure-theoretic properties. We also state some new results relating to energy equality of the NSE. With the exception of a few remarks, the talk should be accessible to anyone who knows some measure theory and a bit of functional analysis. In particular, the necessary background for the NSE will be provided at the beginning of the talk.

Wednesday October 18, 2017 at 4:00 PM in SEO 512