Controllability of systems of Stokes equations with one control force: existence of insensitizing controls

By Sergio Guerrero. 2007

56 citations recorded by the source corpus.

Abstract In this paper we establish some exact controllability results for systems of two parabolic equations of the Stokes kind. In a first part, we prove the existence of insensitizing controls for the L 2 norm of the solutions and the curl of solutions of linear Stokes equations. Then, in the limit case where one can expect null controllability to hold for a system of two Stokes equations (namely, when the coupling terms concern first and second order derivatives, respectively), we prove this result for some general couplings.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Control and Systems Engineering

View Paper: https://www.semanticscholar.org/paper/bb5d4ccbe183be3f97cfc03088836433717eb898

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In Applied Mathematics

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In Control and Systems Engineering

Citations in the corpus

Null controllability of the N-dimensional Stokes system with N−1 scalar controls (2009, unknown): “These ideas were already developed in [8].”
Unique continuation principle for systems of parabolic equations (2010, background): “The results in the previous section give also ε-insensitizing results for the Stokes system (we thank an anonymous referee of this paper for having kindly informed us that the problem of (null) insensitizing control, in the easier case in which ω1 ∩ ω0 = ∅, has been treated by Guerrero in [6]).”
Local null controllability of the three-dimensional Navier–Stokes system with a distributed control having two vanishing components (2012, background): “Remark 6 What is important in the previous proposition is the fact the controls are very regular (which is quite new and interesting in itself) and that the controls are derivatives (in fact curls) of functions, as in [20].”
RECENT RESULTS ON THE CONTROLLABILITY OF LINEAR COUPLED PARABOLIC PROBLEMS: A SURVEY (2011, background): “Further results in this context are the results in [14], where a (slightly) superlinear result was proved, the results of [43], where the author proves some results when the cascade coupling is an operator of first or second order (see Section 7.”
Carleman estimates for parabolic equations and applications (2009, background): “The Carleman estimates for the Navier–Stokes equations have been studied related to the controllability and see [38, 53, 57, 60, 66, 73, 74].”