Optimization problems for the Navier-Stokes equations with regular boundary controls (Q1310374)

This paper deals with questions related to optimal boundary control (with regular controls) for problems governed by the steady Navier-Stokes equations. Here the control is the prescription of the velocity on the boundary (or part of the boundary) of the flow domain. The authors study necessary conditions for an optimal control and justify the use of the Lagrange multiplier rule to derive necessary conditions for optimality. They also study the regularity of the solutions of the optimality system and give some examples of specific optimization problems.