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Optimal control of planar flow of incompressible non-Newtonian fluids. (English) Zbl 1387.76033

Summary: 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.

MSC:

76D55 Flow control and optimization for incompressible viscous fluids
76A05 Non-Newtonian fluids
49J20 Existence theories for optimal control problems involving partial differential equations
49K20 Optimality conditions for problems involving partial differential equations
35Q35 PDEs in connection with fluid mechanics
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References:

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