# Reinhard Farwig

The Navier-Stokes system is the standard model to describe the flow of an incompressible viscous fluid. Although global in time weak solutions can easily be constructed by several methods, it is an open problem in the three-dimensional case whether these solutions are unique, satisfy a physically reasonable energy equality and are strong or even smooth of class $$C^\infty$$.

In this talk we explain this famous Millennium Problem of Clay Mathematics Institute in more details and report on classical results as well as on recent progress.