We study controllability issues for 2D and 3D Navier-Stokes (NS) sys- tems with periodic boundary conditions. The systems are controlled by a degenerate (applied to few low modes) forcing. Methods of differential geometric/Lie algebraic control theory are used to establish global control- lability of finite-dimensional Galerkin approximations of 2D and 3D NS and Euler systems, global controllability in finite-dimensional projection of 2D NS system and L2-approximate controllability for 2D NS system. Beyond these main goals we obtain results on boundedness and contin- uous dependence of trajectories of 2D NS system on degenerate forcing, when the space of forcings is endowed with so called relaxation metric.

Navier--Stokes equations: controllability by means of low modes forcing / Agrachev, Andrey; Sarychev, A.. - In: JOURNAL OF MATHEMATICAL FLUID MECHANICS. - ISSN 1422-6928. - 7:1(2005), pp. 108-152. [10.1007/s00021-004-0110-1]

Navier--Stokes equations: controllability by means of low modes forcing

Agrachev, Andrey;
2005-01-01

Abstract

We study controllability issues for 2D and 3D Navier-Stokes (NS) sys- tems with periodic boundary conditions. The systems are controlled by a degenerate (applied to few low modes) forcing. Methods of differential geometric/Lie algebraic control theory are used to establish global control- lability of finite-dimensional Galerkin approximations of 2D and 3D NS and Euler systems, global controllability in finite-dimensional projection of 2D NS system and L2-approximate controllability for 2D NS system. Beyond these main goals we obtain results on boundedness and contin- uous dependence of trajectories of 2D NS system on degenerate forcing, when the space of forcings is endowed with so called relaxation metric.
2005
7
1
108
152
Agrachev, Andrey; Sarychev, A.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11767/12807
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