  R\"ockner and Zhang in [27] proved the existence of a unique strong solution
to a stochastic tamed 3D Navier-Stokes equation in the whole space and for the
periodic boundary case using a result from [31]. In the latter case, they also
proved the existence of an invariant measure. In this paper, we improve their
results (but for a slightly simplified system) using a self-contained approach.
In particular, we generalise their result about an estimate on the $L^4-$norm
of the solution from the torus to $\mathbb{R}^3$, see Lemma 5.1 and thus
establish the existence of an invariant measure on $\mathbb{R}^3$ for a
time-homogeneous damped tamed 3D Navier-Stokes equation, given by (6.1).

Analysis of PDEs;Probability