The Stokes and NavieraEURO Stokes Equations in Exterior Domains: Moving Domains and Decay Properties

In the first part of this thesis we established a maximal regularity result to the Stokes equations in exterior domains with moving boundary. This leads to existence of solutions to the NavieraEURO Stokes equations globally in time for small data.

Secondly, we consider Leray’s problem on the decay of weak solutions to the NavieraEURO Stokes equations in an exterior domain with non-homogeneous Dirichlet boundary data. It is shown that the solution decays polynomially.