Local null controllability of the two-dimensional Navier–Stokes system in the torus with a control force having a vanishing component
نویسندگان
چکیده
In this paper we deal with the two-dimensional Navier–Stokes system in a torus. The main result establishes the local null controllability with internal controls having one vanishing component. The linearized control system around 0 is not null controllable: the nonlinear term is essential to get this null controllability. Our proof uses the return method together with previous results by Fursikov and Imanuvilov. © 2009 Elsevier Masson SAS. All rights reserved. Résumé Dans cet article on considère le système de Navier–Stokes dans un tore bidimensionnel. Notre résultat principal établit la contrôlabilité locale à zéro avec des contrôles internes ayant une composante nulle. Le système de contrôle linéarisé autour de 0 n’est pas contrôlable : le terme non linéaire est donc essentiel pour obtenir ce résultat. Notre démonstration utilise la méthode du retour combinée avec des résultats précédents de Fursikov et Imanuvilov. © 2009 Elsevier Masson SAS. All rights reserved.
منابع مشابه
Local null controllability of the three-dimensional Navier-Stokes system with a distributed control having two vanishing components
In this paper, we prove a local null controllability result for the three-dimensional Navier-Stokes equations on a (smooth) bounded domain of R with null Dirichlet boundary conditions. The control is distributed into an (arbitrarily small) open subset and has two vanishing components. J.-L. Lions and E. Zuazua proved that the linearized system is not necessarily approximately controllable even ...
متن کاملNull controllability of the N-dimensional Stokes system with N−1 scalar controls
a r t i c l e i n f o a b s t r a c t In this paper we deal with the N-dimensional Stokes system in a bounded domain with Dirichlet boundary conditions. The main result establishes the null controllability with internal controls having one vanishing component. This result improves the one
متن کاملUniqueness Results for Stokes Equations and Their Consequences in Linear and Nonlinear Control Problems
The goal of this article is the study of the approximate controllability for two approximations of Navier Stokes equations with distributed controls The method of proof combines a suitable lin earization of the system with a xed point argument We then are led to study the approximate controllability of linear Stokes systems with potentials We study both the case where there is no constraint on ...
متن کاملControl for Stokes Equations
The goal of this article is the study of the approximate controllability for two approximations of Navier Stokes equations with distributed controls. The method of proof combines a suitable lin-earization of the system with a xed point argument. We then are led to study the approximate controllability of linear Stokes systems with potentials. We study both the case where there is no constraint ...
متن کاملScientific Flow Field Simulation of Cruciform Missiles Through the Thin Layer Navier Stokes Equations
The thin-layer Navier-Stokes equations are solved for two complete missile configurations on an IBM 3090-200 vectro-facility supercomputer. The conservation form of the three-dimensional equations, written in generalized coordinates, are finite differenced and solved on a body-fitted curvilinear grid system developed in conjunction with the flowfield solver. The numerical procedure is based on ...
متن کامل