We consider an optimal control problem for the evolutionary ﬂow of incompressible non-Newtonian ﬂuids in a two-dimensional domain. The existence of optimal controls is proven. Furthermore, we investigate ﬁrst-order necessary as well as second-order suﬃcient optimality conditions. The analysis relies on new results providing solutions with bounded gradients for the ﬂow equations.
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Daniel Wachsmuth, Tomáš Roubíček, Optimal Control of Planar Flow of Incompressible Non-Newtonian Fluids. Z. Anal. Anwend. 29 (2010), no. 3, pp. 351–376DOI 10.4171/ZAA/1412