J. Korean Math. Soc. 2006; 43(1): 45-63
Printed January 1, 2006
Copyright © The Korean Mathematical Society.
Hongchul Kim and Oh-Keun Kwon
Kangnung National University, Kangnung National University
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
© 2022. The Korean Mathematical Society. Powered by INFOrang Co., Ltd