Time-periodic solutions to the navier-stokes equations

Abstract

The Navier-Stokes equations with time-periodic data are investigated with respect to solutions of the same period. In the physical terms, such a system models the flow of a viscous liquid under the influence of a time-periodic force. The three most relevant types of flow domains, from a physical point of view, are considered: a bounded domain, an exterior domain, and an infinite pipe. Methods to show existence of both weak and strong solutions are introduced. Moreover, questions regarding regularity, uniqueness, and asymptotic structure at spatial infinity of solutions are addressed.