## EVENT DETAILS AND ABSTRACT

**PDE Seminar**
**Title:** ON THE ENERGY DISSIPATION IN TURBULENT FLOWS

**Speaker:** Professor A. Shnirelman

**Speaker Info:** Tel-Aviv University

**Brief Description:**

**Special Note**:

**Abstract:**

The talk is devoted to the classical paradox of fluid dynamics. Consider the
motion of a real, slightly compressible and slightly viscous fluid. It seems
obvious that as both compressibility and viscosity of the fluid tend to zero,
the fluid flow approaches the flow of an ideal incompressible fluid; in
particular, the energy dissipation should tend to zero. But experiments show
that the rate of energy dissipation in turbulent flows does not depend on
viscosity, if viscosity is small enough, and is definitely positive. This is a
basic paradox of fluid dynamics.
To solve this paradox, J. Leray introduced weak, or turbulent, solutions of
Navier-Stokes and Euler equations. These are integral identities, expressing
the mass and momentum balance in the fluid. Weak solutions of Euler equations
are especially interesting, because they are expected to describe turbulent
flows where energy is dissipated, while explicit viscosity is absent. But first
examples of weak solutions of Euler equations turned out to be quite
pathological, and had nothing to do with turbulent flows. In 2000, I have
constructed an example of a weak solution with monotonically decreasing
energy; this solution has already some features of turbulence.
I am going to describe this example together with some other examples of
weak solutions, and some related results of P. Constantin and others. No
preliminary knowledge is required.

**Date:** Tuesday, May 01, 2001

**Time:** 3:00pm

**Where:** Lunt 105

**Contact Person:** Prof. Daniel Tataru

**Contact email:** tataru@math.northwestern.edu

**Contact Phone:** 847-467-1838

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