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CONTROLLABILITY OF 2D EULER AND NAVIER-STOKES EQUATIONS BY DEGENERATE FORCING
 

Summary: CONTROLLABILITY OF 2D EULER AND NAVIER-STOKES
EQUATIONS BY DEGENERATE FORCING
ANDREY A. AGRACHEV1
AND ANDREY V. SARYCHEV2
Abstract. We study controllability issues for the 2D Euler and Navier-
Stokes (NS) systems under periodic boundary conditions. These systems
describe motion of homogeneous ideal or viscous incompressible uid on
a two-dimensional torus T2
. We assume the system to be controlled by
a degenerate forcing applied to xed number of modes.
In our previous work [3, 5, 4] we studied global controllability by
means of degenerate forcing for Navier-Stokes (NS) systems with non-
vanishing viscosity ( > 0). Methods of dierential geometric/Lie alge-
braic control theory have been used for that study. In [3] criteria for
global controllability of nite-dimensional Galerkin approximations of
2D and 3D NS systems have been established. It is almost immediate
to see that these criteria are also valid for the Galerkin approximations
of the Euler systems. In [5, 4] we established a much more intricate suf-
cient criteria for global controllability in nite-dimensional observed
component and for L2-approximate controllability for 2D NS system.

  

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

 

Collections: Engineering; Mathematics