  The equations of stationary compressible flows of active liquid crystals are
considered in a bounded three-dimensional domain. The system consists of the
stationary Navier-Stokes equations coupled with the equation of Q-tensors and
the equation of the active particles. The existence of weak solutions to the
stationary problem is established through a two-level approximation scheme,
compactness estimates and weak convergence arguments. Novel techniques are
developed to overcome the difficulties due to the lower regularity of
stationary solutions, a Moser-type iteration is used to deal with the strong
coupling of active particles and fluids, and some weighted estimates on the
energy functions are achieved so that the weak solutions can be constructed for
all values of the adiabatic exponent $\gamma>1$.
