Korean J. Math. Vol. 23 No. 2 (2015) pp.293-312
DOI: https://doi.org/10.11568/kjm.2015.23.2.293

A boundary control problem for vorticity minimization in time-dependent 2D Navier-Stokes equations

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Published: Jun 30, 2015
Keywords:
Navier-Stokes equations, boundary control, vorticity minimization.
Mathematics Subject Classification:
35Q30, 49J20, 49J50, 76F70.

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Hongchul Kim
Department of Mathematics Gangneung-Wonju National University Gangneung 210-702, Korea

Abstract

We deal with a boundary control problem for the vorticity minimization, in which the flow is governed by the time-dependent two dimensional incompressible Navier-Stokes equations. We derive a mathematical formulation and a process for an appropriate control along the portion of the boundary to minimize the vorticity motion due to the flow in the fluid domain. After showing the existence of an optimal solution, we derive the optimality system for which optimal solutions may be determined. The differentiability of the state solution in regard to the control parameter shall be conjunct with the necessary conditions for the optimal solutions.


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