Periodic and Almost Periodic Solutions to Fluid Flow Problems

This mini-course introduces a general approach to study the existence and uniqueness of time-periodic and almost periodic solutions to incompressible fluid flow problems and semi-linear evolution equations. The method developed here is based on a combination of interpolation spaces and topological arguments, as well as on the Lp-Lq smoothing properties of the linearized equations, and some other standard techniques for construction of solution operators.  It yields, on the one hand, a unified approach to various classical problems in incompressible fluid flow and, on the other hand, gives new results for periodic and almost periodic solutions to the Navier–Stokes–Oseen flow, the Navier–Stokes flow past rotating obstacles, as well as to stratified flows.