Exact controllability in projections for three-dimensional Navier-Stokes equations

Abstract

The paper is devoted to studying controllability properties for 3D Navier-Stokes equations in a bounded domain. We establish a sufficient condition under which the problem in question is exactly controllable in any finite-dimensional projection. Our sufficient condition is verified for any torus in $R^3$. The proofs are based on a development of a general approach introduced by Agrachev and Sarychev in the 2D case. As a simple consequence of the result on controllability, we show that the Cauchy problem for the 3D Navier-Stokes system has a unique strong solution for any initial function and a large class of external forces.

24 pages

References in corpus (1)

• Controllability of 2D Euler and Navier-Stokes Equations by Forcing 4 Modes

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