  A key ingredient of our fictitious domain, higher order space-time cut finite
element (CutFEM) approach for solving the incompressible Navier--Stokes
equations on evolving domains (cf.\ \cite{Bause2021}) is the extension of the
physical solution from the time-dependent flow domain $\Omega_f^t$ to the
entire, time-independent computational domain $\Omega$. The extension is
defined implicitly and, simultaneously, aims at stabilizing the discrete
solution in the case of unavoidable irregular small cuts. Here, the convergence
properties of the scheme are studied numerically for variations of the combined
extension and stabilization.
