Local exact controllability of the Navier-Stokes system ✩

By Enrique Fernández-Cara, Sergio Guerrero, Oleg Yu. Imanuvilov, Jean-Pierre Puel. 2004

196 citations recorded by the source corpus.

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

View Paper: https://www.semanticscholar.org/paper/6bb0f46047a12fb619f1698ca64bf9251028bdc0

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Citations in the corpus

Null controllability of the N-dimensional Stokes system with N−1 scalar controls (2009, background): “Let us remark that, even in the case of N scalar controls, our proof of (2) is simpler than the ones given in [9] and [ 4 ]: in these papers, a local estimate of the pressure had to be performed.”
Carleman estimates for one-dimensional degenerate heat equations (2006, background): “Controllability properties of nondegenerate parabolic equations have been widely studied in recent years; concerning the heat equation, see in particular [2, 5, 10, 13, 14, 15, 16, 17, 19, 24, 25, 27, 28, 29, 32, 33]; concerning the Stokes and Navier-Stokes equations, see in particular [3, 18, 19, 2”
Carleman estimates for parabolic equations with nonhomogeneous boundary conditions (2009, background): “right-hand sides, sharp Carleman estimates have been obtained in [12] and this result turned out to be essential for obtaining estimates on the pressure in the context of controllability for the Navier-Stokes equations (see [ 5 ]).”
Local null controllability of the three-dimensional Navier–Stokes system with a distributed control having two vanishing components (2012, methodology): “In fact, using the same arguments as in [15] and [16] (see also [6, Remark 1]), one can easily extend the previous theorem to small initial data in H ∩ L4(Ω)3 with a solution (y, p) ∈ L2((0, T ), V ) ∩ L∞((0, T ), H) × L2(Q).”
Controllability of systems of Stokes equations with one control force: existence of insensitizing controls (2007, unknown): “In a similar form, this lemma was proved in [ 6 ].”
Feedback stabilization of the 2-D and 3-D Navier-Stokes equations based on an extended system (2009, background): “30) An exact controllability result [9] ensures the existence of a finite time T0 ∈ ]0,∞[, and of a control fT0 ∈ L2(0,∞;L2(Ω̃)) supported in ω1 × (0, T0) for which the solution to (10.”
On the Fattorini criterion for approximate controllability and stabilizability of parabolic systems (2014, methodology): “Or the work of Raymond and Thevenet [43] where the exact controllability of the finite dimensional unstable projected system is deduced from the stabilizability by infinite dimensional control proved in [42], itself relying on the null controllability of the Oseen equations [21].”
Local exact controllability to the trajectories of the 1-D Kuramoto–Sivashinsky equation☆ (2011, unknown): “It has been done by using either internal controls (see [9,14,15,10,13]) or boundary controls (see [12,25]).”
RECENT RESULTS ON THE CONTROLLABILITY OF LINEAR COUPLED PARABOLIC PROBLEMS: A SURVEY (2011, background): “[19], [38], [34], [35], [21], [29] and [18] for fluids and [51], [55] and [12] in the case of thermoelastic systems (see also the bibliography therein).”