Differential equations are a fundamental tool for modeling processes in science and technology. This lecture first introduces the Bochner integral and weak derivatives for functions with values in Banach spaces. Then we will look at different evolution equations with linear and monotone operators. We consider the time-dependent Navier-Stokes equations and show the existence of strong solutions locally in time, weak solutions globally in time, and their weak-strong uniqueness. Finally, we review some selected trends in research on partial differential equations.
This lecture is connected to the lecture Nonlinear Evolution Equations and it is strongly recommended to take both modules together. The lecture is a BMS course and is held in English. This course can also serve as a basis for a master thesis in the field of differential equations.
Literature
Will be announced.