Conformal mappings and fluid flows

V svoji diplomski nalogi sem se ukvarjal z mehaniko tekočin. V prvem delu sem svojo analizo omejil na idealne tekočine, fluide, katerih tokovnice lahko ponazorimo z dvodimenzionalnimi vektorskimi polji brez izvorov in vrtincev. Dokazal sem, da lahko le-te povežemo s teorijo holomorfnih funkcij, ter nato s pomočjo Riemannovega upodobitvenega izreka tokove okoli zapletenih objektov reduciramo na nekatere elementarne primere. V zadnjem delu naloge sem nato dodatno predstavil tudi Blasiousov izrek in nekaj primerov ne-idealnih tokov, ki pa generirajo vzgon.In my thesis I dealt with fluid mechanics. In first part of my analysis I focused on ideal fluids. These are fluids, whose streamlines can be represented with twodimenzional vector fields without sources and vortices. I proved that such vector fields can be connected to theory of holomorphic functions. Using Riemann mapping theorem, flows around complicated objects can be reduced to elementary examples. In last part I also additionally presented Blasius theorem and some non-ideal flow examples, which do produce lift