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

Annales de l'Institut Henri Poincare (C) Non Linear Analysis, 2007, Volume 24, Issue 4, Pages 521-537 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 exactl...

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Bibliographic Details
Main Author Shirikyan, Armen
Format Journal Article
LanguageEnglish
Published 27.12.2005
Subjects
Mathematics - Analysis of PDEs
Mathematics - Optimization and Control
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Summary:Annales de l'Institut Henri Poincare (C) Non Linear Analysis, 2007, Volume 24, Issue 4, Pages 521-537 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.
DOI:10.48550/arxiv.math/0512600