Injection-suction control for two-dimensional Navier-Stokes equations with slippage

Nikolai Chemetov; Fernanda Cipriano

doi:10.1137/17M1121196

Injection-suction control for two-dimensional Navier-Stokes equations with slippage

Nikolai Chemetov, Fernanda Cipriano

Research output: Contribution to journal › Article › peer-review

5 Citations (Scopus)

Abstract

We consider a velocity tracking problem for the Navier-Stokes equations in a 2D bounded domain. The control acts on the boundary through an injection-suction device, and the flow is allowed to slip against the surface wall. We study the well-posedness of the state equations, linearized state equations, and adjoint equations. In addition, we show the existence of an optimal solution and establish the first order optimality condition.

Original language	English
Pages (from-to)	1253-1281
Number of pages	29
Journal	SIAM Journal on Control and Optimization
Volume	56
Issue number	2
DOIs	https://doi.org/10.1137/17M1121196
Publication status	Published - 1 Jan 2018

Keywords

Navier slip boundary conditions
Navier-Stokes equations
Optimal control

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10.1137/17M1121196

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title = "Injection-suction control for two-dimensional Navier-Stokes equations with slippage",

abstract = "We consider a velocity tracking problem for the Navier-Stokes equations in a 2D bounded domain. The control acts on the boundary through an injection-suction device, and the flow is allowed to slip against the surface wall. We study the well-posedness of the state equations, linearized state equations, and adjoint equations. In addition, we show the existence of an optimal solution and establish the first order optimality condition.",

keywords = "Navier slip boundary conditions, Navier-Stokes equations, Optimal control",

author = "Nikolai Chemetov and Fernanda Cipriano",

note = "The second author's work was partially supported by the Fundacao para a Ciencia e a Tecnologia (Portuguese Foundation for Science and Technology) through project UID/MAT/00297/2013 (Centro de Matematica e Aplicacoes).",

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AU - Cipriano, Fernanda

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N2 - We consider a velocity tracking problem for the Navier-Stokes equations in a 2D bounded domain. The control acts on the boundary through an injection-suction device, and the flow is allowed to slip against the surface wall. We study the well-posedness of the state equations, linearized state equations, and adjoint equations. In addition, we show the existence of an optimal solution and establish the first order optimality condition.

AB - We consider a velocity tracking problem for the Navier-Stokes equations in a 2D bounded domain. The control acts on the boundary through an injection-suction device, and the flow is allowed to slip against the surface wall. We study the well-posedness of the state equations, linearized state equations, and adjoint equations. In addition, we show the existence of an optimal solution and establish the first order optimality condition.

KW - Navier slip boundary conditions

KW - Navier-Stokes equations

KW - Optimal control

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JF - SIAM Journal on Control and Optimization

IS - 2

ER -

Injection-suction control for two-dimensional Navier-Stokes equations with slippage

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Keywords

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