  It is shown that the magnetohydrodynamic equilibrium states of an
axisymmetric toroidal plasma with finite resistivity and flows parallel to the
magnetic field are governed by a second-order partial differential equation for
the poloidal magnetic flux function $\psi$ coupled with a Bernoulli type
equation for the plasma density (which are identical in form to the
corresponding ideal MHD equilibrium equations) along with the relation
$\Delta^\star \psi=V_c \sigma$. (Here, $\Delta^\star$ is the
Grad-Schl\"{u}ter-Shafranov operator, $\sigma$ is the conductivity and $V_c$ is
the constant toroidal-loop voltage divided by $2 \pi $). In particular, for
incompressible flows the above mentioned partial differential equation becomes
elliptic and decouples from the Bernoulli equation [H. Tasso and G. N.
Throumoulopoulos, Phys. Plasmas {\bf 5}, 2378 (1998)]. For a conductivity of
the form $\sigma=\sigma(R, \psi)$ ($R$ is the distance from the axis of
symmetry) several classes of analytic equilibria with incompressible flows can
be constructed having qualitatively plausible $\sigma$ profiles, i.e. profiles
with $\sigma$ taking a maximum value close to the magnetic axis and a minimum
value on the plasma surface. For $\sigma=\sigma(\psi)$ consideration of the
relation $\Delta^\star\psi = V_c \sigma(\psi)$ in the vicinity of the magnetic
axis leads therein to a proof of the non-existence of either compressible or
incompressible equilibria. This result can be extended to the more general case
of non-parallel flows lying within the magnetic surfaces.
