Decision and Control Lecture Series

Decision and Control Laboratory, Coordinated Science Laboratory

Controlling Velocities and Domains of the Incompressible Fluid

by Means of Degenerate Distributed Forcing

Professor Andrey Sarychev

Department of Mathematics for Decisions

Florence University

Wednesday, March 6, 2013

3:00 p.m. to 4:00 p.m.

B02 Auditorium CSL

Abstract

In our previous work with A. Agrachev (2004-08) we studied controllability issues for the 2D Euler and Navier-Stokes (NS) systems, which describe the evolution of the velocity field for the motion of homogeneous ideal or viscous incompressible fluid on a two-dimensional domain (such as torus, sphere, hemisphere, Riemannian surface). We assumed the system to be controlled by a forcing, which is a linear combination of few functions on the domain (modes) with time-variant coefficients, which are interpreted as controls. Such forcing is called degenerate.

We managed to show that one can choose a small universal set of controlled modes, such that controls, applied to them, are able to provide –approximate controllability for Navier-Stokes/Euler equation as well as global controllability in projections on any finite-dimensional subspace in the space of velocities (or vorticities).

(Please see flyer for additional information)

References

[1] Agrachev A.A., A.V.Sarychev, Solid Controllability in Fluid Dynamics. In: C. Bardos, A. Fursikov Eds., "Instability in Models Connected with Fluid Flows I", Springer, 2008, pp.1-35.