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DCL Lecture Series: Professor Andrey Sarychev, Controlling Velocities and Domains of the Incompressible Fluid by Means of Degenerate Distributed Forcing

Speaker Professor Andrey Sarychev, Florence University
Date Mar 6, 2013
Time 3:00 pm - 4:00 pm  
Location CSL Auditorium (B02 CSL)
Sponsor Decision and Control Laboratory, Coordinated Science Laboratory
Contact Angie Ellis
Phone 217/300-1910
Event type seminar
Views 1194
Originating Calendar CSL Decision and Control Group

 

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).

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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.

 

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