Stationary anisotropic Stokes, Oseen and Navier–Stokes systems: Periodic solutions in ℝn

Abstract

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 in . By the Galerkin algorithm and the Brower fixed point theorem, the existence of solution to the stationary anisotropic (nonlinear) Navier–Stokes incompressible system is shown in a periodic Sobolev space for any . Then the solution uniqueness and regularity results for stationary anisotropic periodic Navier–Stokes system are established for .