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2009, Volume 11, Issue 2: 283-314. Doi: 10.3934/dcdsb.2009.11.283
This issue Previous Article Semi-discretization in time for nonlinear Zakharov waves equations Next Article Mixed generalized Laguerre-Fourier spectral method for exterior problem of Navier-Stokes equations

Boundary velocity suboptimal control of incompressible flow in cylindrically perforated domain

  • 1.

    Università di Salerno, DIIMA, Via Ponte don Melillo, 84084 Fisciano (SA)

  • 2.

    Dipartimento di Matematica e Applicazioni, Università degli Studi di Napoli “Federico II”, DMA “R. Caccioppoli”, Complesso Monte S. Angelo, via Cintia, 80126 Napoli

  • 3.

    Dnipropetrovsk National University, Department of Differential Equations, Kozakov str., 18/14, 49050 Dnipropetrovsk

Received:  September 30, 2007
Revised:  February 29, 2008
Published:  August 2009
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    Abstract
  • In this paper we study an optimal boundary control problem for the 3D steady-state Navier-Stokes equation in a cylindrically perforated domain $\Omega_{\epsilon}$. The control is the boundary velocity field supported on the 'vertical' sides of thin cylinders. We minimize the vorticity of viscous flow through thick perforated domain. We show that an optimal solution to some limit problem in a non-perforated domain can be used as basis for the construction of suboptimal controls for the original control problem. It is worth noticing that the limit problem may take the form of either a variational calculation problem or an optimal control problem for Brinkman's law with another cost functional, depending on the cross-size of thin cylinders.
    Mathematics Subject Classification: Primary: 35Q30, 49J20; Secondary: 35B27, 35B40.

    Citation:
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