  In this paper, we prove global existence of weak solutions for the stationary
compressible Navier-Stokes equations with an anisotropic and nonlocal viscous
term in a periodic domain. This gives an answer to an open problem important
for applications in geophysics or in microuidics. The main idea is to adapt in
a non-trivial way the new idea developped by the authors in a previous paper,
see [2] which allowed them to treat the anisotropic compressible
quasi-stationary Stokes system.
