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SOLID CONTROLLABILITY IN FLUID DYNAMICS ANDREY A. AGRACHEV1
 

Summary: SOLID CONTROLLABILITY IN FLUID DYNAMICS
ANDREY A. AGRACHEV1
AND ANDREY V. SARYCHEV2
Abstract. We survey results of recent activity towards studying con-
trollability and accessibility issues for equations of dynamics of incom-
pressible uids controlled by low-dimensional or, degenerate, forcing.
New results concerning controllability of Navier-Stokes/Euler systems
on two-dimensional sphere and on generic two-dimensional domain are
represented.
Keywords: incompressible uid, 2D Euler system, 2D Navier-Stokes
system, controllability
AMS Subject Classication: 35Q30, 93C20, 93B05, 93B29
1. Introduction
We survey results of recent activity aimed at studying controllability and
accessibility properties of Navier-Stokes systems (NS systems) controlled by
low-dimensional (degenerate) forcing. This choice of control is characteristic
feature of our problem setting. The corresponding equations are
u/t + uu + gradp = u + F(t, x),(1)
divu = 0.(2)
The words "degenerate forcing" mean that F(t, x) can be represented as:

  

Source: Agrachev, Andrei - Functional Analysis Sector, Scuola Internazionale Superiore di Studi Avanzati (SISSA)

 

Collections: Engineering; Mathematics