### Thursday, July 16

## SS5

The W. T. and Idalia Reid Prize

On the Control of Navier Stokes Equations

5:45 PM-6:30 PM

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

*Room: Convocation Hall*

The W. T. and Idalia Reid Prize in Mathematics is awarded for research in, or other contributions to, the broadly defined areas of differential equations and control theory. Each prize may be given either for a single notable achievement or for a collection of such achievements. The prize winner and speaker is Jacques-Louis Lions.

The speaker will consider the Navier Stokes equations with a control acting either inside the domain or, more realistically, on part of the boundary. He conjectured in 1990 that this system is **approximately controllable.** Important contributions to the proof of the conjecture have been made by J. M. Coron and F. Fursikov and Yu. Imanuvilov. After giving some of these results, the speaker will address the question of finding **numerical approximations** of these controls achieving approximate controllability and, in particular, **real time numerical approximations.**

A systematic method will be presented, based on domain decomposition and on new ways of decomposition of domains, spaces and operators.

*(This is based on work by O. Pironneau and the A., being published in the CRAS.)*

**Jacques-Louis Lions**

*Collège de France, France*

LMH Created: 3/16/98; MMD Updated: 5/19/98