  Cahn-Hilliard-Navier-Stokes system describes the evolution of two isothermal,
incompressible, immiscible fluids in a bounded domain. In this work, we
consider the stationary nonlocal Cahn-Hilliard-Navier-Stokes system in two and
three dimensions with singular potential. We prove the existence of a weak
solution for the system using pseudo-monotonicity arguments and Browder's
theorem. Further we establish the uniqueness and regularity results for the
weak solution of the stationary nonlocal Cahn-Hilliard-Navier-Stokes system for
constant mobility parameter and viscosity. Finally, in two dimensions, we
establish that the stationary solution is exponentially stable under suitable
conditions on mobility parameter and viscosity.
