### Wednesday, July 15

## SS2

The John von Neumann Lecture

On Some Descriptions of the Dynamics of Viscous Fluids

4:30 PM-5:30 PM

*Chair: John Guckenheimer, President, SIAM; and Cornell University*

*Room: Convocation Hall *

The lecturer will discuss some problems connected with description of the dynamics of viscous fluids by the Navier-Stokes and by the Modified Navier-Stokes equations with the coefficients of viscosity depending on the strain velocity tensor.

For example: (1). Do the Navier-Stokes equations yield a deterministic description
of the viscous fluids dynamics for all values of the Reynolds number or not? (2). What numerical experiments can demonstrate the collapse of a solution to the Navier-Stokes equations? (3). There are classes of the Modified Navier-Stokes equations that give deterministic description of the dynamics of viscous fluids for arbitrary velocity gradients. For them the results on a global unique solvability of the principal boundary-value problems, as well as the existence of compact minimal B-attractors will be formulated. Some approximations to the Modified Navier-Stokes equations will be suggested and the problems of their smoothness will be discussed.

**Olga A. Ladyzhenskaya**

*Steklov Mathematics Institute*

*Russian Academy of Sciences, Russia*

MMD Created: 4/6/98 Updated: 4/6/98