  We analyse a Eulerian Finite Element method, combining a Eulerian
time-stepping scheme applied to the time-dependent Stokes equations using the
CutFEM approach with inf-sup stable Taylor-Hood elements for the spatial
discretisation. This is based on the method introduced by Lehrenfeld \&
Olshanskii [ESAIM: M2AN 53(2):585--614] in the context of a scalar
convection-diffusion problems on moving domains, and extended to the
non-stationary Stokes problem on moving domains by Burman, Frei \& Massing
[arXiv:1910.03054 [math.NA]] using stabilised equal-order elements. The
analysis includes the geometrical error made by integrating over approximated
levelset domains in the discrete CutFEM setting. The method is implemented and
the theoretical results are illustrated using numerical examples.
