Journal of the
Korean Mathematical Society
JKMS

ISSN(Print) 0304-9914 ISSN(Online) 2234-3008

Article

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J. Korean Math. Soc. 2006; 43(1): 45-63

Printed January 1, 2006

Copyright © The Korean Mathematical Society.

On a vorticity minimization problem for the stationary 2D Stokes equations

Hongchul Kim and Oh-Keun Kwon

Kangnung National University, Kangnung National University

Abstract

This paper is concerned with a boundary control problem for the vorticity minimization, in which the flow is governed by the stationary two dimensional Stokes equations. We wish to find a mathematical formulation and a relevant process for an appropriate control along the part of the boundary to minimize the vorticity due to the flow. After showing the existence and uniqueness of an optimal solution, we derive the optimality conditions. The differentiability of the state solution in regard to the control parameter shall be conjunct with the necessary conditions for the optimal solution. For the minimizer, an algorithm based on the conjugate gradient method shall be proposed.

Keywords: Stokes equations, boundary control, vorticity minimization, conjugate gradient algorithm

MSC numbers: 49J20, 49J50, 76F70