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

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

2005-12-27

arxiv.org/abs/math/0512600v1

Mathematics

Analysis of PDEs

24 pages

Scientific paper

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.

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