Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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ON A VORTICITY MINIMIZATION PROBLEM FOR THE STATIONARY 2D STOKES EQUATIONS

  • KIM HONGCHUL (Department of Mathematics Kangnung National University) ;
  • KWON OH-KEUN (Department of Mathematics Kangnung National University)
  • Published : 2006.01.01
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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.

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References

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Cited by

  1. A BOUNDARY CONTROL PROBLEM FOR VORTICITY MINIMIZATION IN TIME-DEPENDENT 2D NAVIER-STOKES EQUATIONS vol.23, pp.2, 2015, https://doi.org/10.11568/kjm.2015.23.2.293