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Communications in Mathematical Physics

, Volume 266, Issue 1, pp 123–151 | Cite as

Approximate Controllability of Three-Dimensional Navier–Stokes Equations

  • Armen Shirikyan
Article

Abstract

The paper is devoted to studying the problem of controllability for 3D Navier–Stokes equations in a bounded domain. We develop the method introduced by Agrachev and Sarychev in the 2D case and establish a sufficient condition under which the problem in question is approximately controllable by a finite-dimensional force. In the particular case of a torus, it is shown that our sufficient condition is fulfilled for a control of low dimension not depending on the viscosity.

Keywords

Stokes Equation Implicit Function Theorem Stokes System Piecewise Constant Function Exact Controllability 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag 2006

Authors and Affiliations

  1. 1.Laboratoire de MathématiquesUniversité de Paris-Sud XIOrsay CedexFrance.

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