In this thesis we consider two nonlinear, time and space dependent systems of partial differential equations stemming from fluid dynamics and from chemical engineering on nonsmooth domains. While the first part is devoted to the Navier-Stokes equations on a wedge domain, in the second part a model of heterogeneous catalysis on a finite cylinder is considered. The aim of this thesis is to give an analytic approach for both systems under consideration. We show strong local-in-time well-posedness results for both systems and a strong global-in-time result for the catalysis model.
