Appl Math Optim DOI 10.1007/s00245-014-9240-x On the Approximate Controllability of Stackelberg–Nash Strategies for Linearized Micropolar Fluids F. D. Araruna · S. D. B. de Menezes · M. A. Rojas-Medar © Springer Science+Business Media New York 2014 Abstract We study a Stackelberg strategy subject to the evolutionary linearized micropolar fluids equations, considering a Nash multi-objective equilibrium (non nec- essarily cooperative) for the “follower players” (as is called in the economy field) and an optimal problem for the leader player with approximate controllability objective. We will obtain the following three main results: the existence and uniqueness of Nash equilibrium and its characterization, the approximate controllability of the linearized micropolar system with respect to the leader control, and the existence and unique- ness of the Stackelberg–Nash problem, where the optimality system for the leader is given. Keywords Micropolar fluids · Stackelberg–Nash strategies · Controllability Mathematics Subject Classfication 35K20 · 93B05 · 76D55 F. D. Araruna Departamento de Matemática, Universidade Federal da Paraíba, João Pessoa, PB 58051-900, Brazil e-mail: fagner@mat.ufpb.br S. D. B. de Menezes Departamento de Matemática, Universidade Federal do Ceará, Fortaleza, CE 60455-760, Brazil e-mail: silvano@mat.ufc.br M. A. Rojas-Medar (B ) Grupo de Matemática Aplicada, Dpto. de Ciencias Básicas, Facultad de Ciencias, Universidad del Bío-Bío, Campus Fernando May, Casilla 447, Chillán, Chile e-mail: marko@ueubiobio.cl 123