Local null controllability of the \(N\)-dimensional Navier-Stokes system with nonlinear Navier-slip boundary conditions and \(N-1\) scalar controls

DOI10.1016/j.matpur.2018.03.004zbMath1388.35144OpenAlexW2793602955MaRDI QIDQ1746485

Cristhian Montoya, Sergio Guerrero

Publication date: 25 April 2018

Published in: Journal de Mathématiques Pures et Appliquées. Neuvième Série (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.matpur.2018.03.004

zbMATH Keywords

Carleman estimatesnull controllabilityNavier-Stokes systemNavier-slip boundary conditions

Mathematics Subject Classification ID

Controllability (93B05) Nonlinear systems in control theory (93C10) Navier-Stokes equations (35Q30) A priori estimates in context of PDEs (35B45) Existence, uniqueness, and regularity theory for incompressible viscous fluids (76D03)

Related Items (9)

Local null controllability of the penalized Boussinesq system with a reduced number of controls ⋮ Controllability results for cascade systems of m coupled N-dimensional stokes and Navier-stokes systems by N – 1 scalar controls ⋮ Existence of controls insensitizing the rotational of the solution of the Navier-Stokes system having a vanishing component ⋮ Uniform Controllability of a Stokes Problem with a Transport Term in the Zero-Diffusion Limit ⋮ RBF collocation and hybrid-LHI methods for Stokes systems and its application to controllability problems ⋮ Local exact controllability to the trajectories of the Korteweg-de Vries-Burgers equation on a bounded domain with mixed boundary conditions ⋮ Local null controllability of a fluid–rigid body interaction problem with Navier slip boundary conditions ⋮ Remarks on local controllability for the Boussinesq system with Navier boundary condition ⋮ Global Carleman estimate and its applications for a sixth-order equation related to thin solid films

Cites Work

• Local null controllability of the three-dimensional Navier-Stokes system with a distributed control having two vanishing components
• Theoretical and numerical local null controllability of a Ladyzhenskaya-Smagorinsky model of turbulence
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• Mathematical tools for the study of the incompressible Navier-Stokes equations and related models
• Local exact controllability of the Navier-Stokes system
• Local controllability of the \(N\)-dimensional Boussinesq system with \(N - 1\) scalar controls in an arbitrary control domain
• Local null controllability of the \(N\)-dimensional Navier-Stokes system with \(N - 1\) scalar controls in an arbitrary control domain
• Local exact controllability of micropolar fluids
• On the local exact controllability of micropolar fluids with few controls
• On the controllability of the 2-D incompressible Navier-Stokes equations with the Navier slip boundary conditions
• Null controllability of the heat equation with boundary Fourier conditions: the linear case
• Local exact controllability to the trajectories of the Navier-Stokes system with nonlinear Navier-slip boundary conditions
• Set-valued analysis
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