  First, the solution uniqueness, existence and regularity for stationary
anisotropic (linear) Stokes and generalised Oseen systems with constant
viscosity coefficients in a compressible framework are analysed in a range of
periodic Sobolev (Bessel-potential) spaces on $n$-dimensional flat torus. By
the Galerkin algorithm, the linear results are employed to show existence of
solution to the stationary anisotropic (non-linear) Navier-Stokes
incompressible system on torus in a periodic Sobolev space for any $n\ge 2$.
Then the solution uniqueness and regularity results for stationary anisotropic
Navier-Stokes system on torus are established for $n\in\{2,3,4\}$.
