Remarks on exact controllability for the Navier-Stokes equations

By Oleg Yu. Imanuvilov. 2001

180 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Control and Systems Engineering, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/14d0c4a2c365b3b21ebced3769eb7d7314a25d26

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In Computational Theory and Mathematics

In Control and Systems Engineering

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Citations in the corpus

Local null controllability of the three-dimensional Navier–Stokes system with a distributed control having two vanishing components (2012, background): “Let g ∈ C ∞ ( R 3 ) , g : ( t, w, x 3 ) (cid:55)→ g ( t, w, x 3 ) , and h ∈ C ∞ ( R 3 ) , h : ( t, w, x 3 ) (cid:55)→ h ( t, w, x 3 ) .”
Estimates on the generalization error of physics-informed neural networks for approximating a class of inverse problems for PDEs (2020, background): “Although some Carleman estimates, leading to conditional stability bounds, are available for the Navier-Stokes equations [26], applying them to derive bounds on the generalization error is very challenging and will be considered in a forthcoming paper.”
Local exact controllability of the Navier-Stokes system ✩ (2004, methodology): “However, the plan of the proof follows the one in [ 10 ] and contains four parts.”
Global Carleman estimates for weak solutions of elliptic nonhomogeneous Dirichlet problems (2002, background): “On the other hand, global Carleman inequalities have been given by [2], then by [4] and [5], in the context of controllability problems, for solutions of elliptic (and parabolic) equations when the right-hand side is element of L 2 .”
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].”
Controllability of systems of Stokes equations with one control force: existence of insensitizing controls (2007, unknown): “for the solutions of (7) and (8), where m is some positive number and C and C0 are two positive constants depending on Ω,ω,O, T , a and B but independent of ψ0 (see, for instance, [11] or [9]).”