Topics in Mathematical Fluid Mechanics and Shape Optimization
Technical university of Liberec
This habilitation thesis is based on the author's contributions to the mathematical theory of incompressible uids and to the shape optimization in uid mechanics. In Chapter 2, an overview of basic equations, theory of weak solutions and nite-element approximation for incompressible uids is given. Chapter 3 is devoted to the formulation of shape optimization problems, to the questions of existence of solutions, approximation and di erentiability. Finally, in Chapter 4 some results obtained by the author are mentioned, namely on the theory of non-Newtonian piezoviscous uids, applied shape optimization and sensitivity analysis.