Local exact controllability to the trajectories of the Navier-Stokes system with nonlinear Navier-slip boundary conditions

DOI10.1051/cocv:2006006zbMath1106.93011OpenAlexW2025311076MaRDI QIDQ3416751

Sergio Guerrero

Publication date: 22 January 2007

Published in: ESAIM: Control, Optimisation and Calculus of Variations (Search for Journal in Brave)

Full work available at URL: http://www.numdam.org/item?id=COCV_2006__12_3_484_0

zbMATH Keywords

controllabilityNavier-Stokes systemslip

Mathematics Subject Classification ID

Controllability (93B05) Nonlinear systems in control theory (93C10) Navier-Stokes equations (35Q30) Existence theories for optimal control problems involving partial differential equations (49J20)

Related Items (12)

Global Controllability of the Boussinesq System with Navier-Slip-with-Friction and Robin Boundary Conditions ⋮ Small-time global exact controllability of the Navier-Stokes equation with Navier slip-with-friction boundary conditions ⋮ Controllability results for cascade systems of m coupled N-dimensional stokes and Navier-stokes systems by N – 1 scalar controls ⋮ Local exact controllability to the trajectories of the 1-D Kuramoto-Sivashinsky equation ⋮ Approximate controllability for linearized compressible barotropic Navier-Stokes system in one and two dimensions ⋮ Uniform Controllability of a Stokes Problem with a Transport Term in the Zero-Diffusion Limit ⋮ Local null controllability of the \(N\)-dimensional Navier-Stokes system with nonlinear Navier-slip boundary conditions and \(N-1\) scalar controls ⋮ Local null controllability of a fluid–rigid body interaction problem with Navier slip boundary conditions ⋮ On the global null controllability of a Navier-Stokes system with Navier slip boundary conditions ⋮ Smooth controllability of the Navier-Stokes equation with Navier conditions: application to Lagrangian controllability ⋮ Observability and unique continuation of the adjoint of a linearized simplified compressible fluid-structure model in a 2d channel ⋮ Remarks on local controllability for the Boussinesq system with Navier boundary condition

Cites Work

• On a boundary value problem for a stationary system of Navier-Stokes equations
• Null and approximate controllability for weakly blowing up semilinear heat equations
• Local exact controllability of the Navier-Stokes system
• Remarks on exact controllability for the Navier-Stokes equations
• On the controllability of the 2-D incompressible Navier-Stokes equations with the Navier slip boundary conditions
• Approximate controllability of the semilinear heat equation
• Null controllability of nonlinear convective heat equations
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