Existence of an Optimal Solution of a Shape Control Problem for the Stationary Navier--Stokes Equations

Authors:
Max D. Gunzburger;Hongchul Kim
Affiliations:
-;-
Venue:
SIAM Journal on Control and Optimization
Year:
1998

Citing 0
Cited 1

Shape-topology optimization for Navier-Stokes problem using variational level set method

Journal of Computational and Applied Mathematics

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Abstract

This paper is concerned with an optimal shape control problem for the stationary Navier--Stokes system. A two-dimensional channel flow of an incompressible, viscous fluid is examined to determine the shape of a bump on a part of the boundary that minimizes the viscous drag. After giving a precise formulation of the extremal problem in a function analytic setting, it is shown that optimal solutions exist.