Communications in Mathematical Physics

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

Approximate Controllability of Three-Dimensional Navier–Stokes Equations

  • Armen Shirikyan


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.


Stokes Equation Implicit Function Theorem Stokes System Piecewise Constant Function Exact Controllability 
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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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