PDE Seminar

Speaker: Professor A. Shnirelman
Speaker Info: Tel-Aviv University
Brief Description:
Special Note:

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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