  Stokes flow equations, used to model creeping flow, are a commonly used
simplification of the Navier--Stokes equations. The simplification is valid for
flows where the inertial forces are negligible compared to the viscous forces.
In infinite domains, this simplification leads to a fundamental paradox.
  In this work we review the Stokes paradox and present new insights related to
recent research. We approach the paradox from three different points of view:
modern functional analysis, numerical simulations, and classical analytic
techniques. The first approach yields a novel, rigorous derivation of the
paradox. We also show that relaxing the Stokes no-slip condition (by
introducing a Navier's friction condition) in one case resolves the Stokes
paradox but gives rise to d'Alembert's paradox.
  The Stokes paradox has previously been resolved by Oseen, who showed that it
is caused by a limited validity of Stokes' approximation. We show that the
paradox still holds for the Reynolds--Orr equations describing kinetic energy
flow instability, meaning that flow instability steadily increases with domain
size. We refer to this as an instability paradox.
