Asymptotics of solutions of the stationary Navier–Stokes system of equations in a domain of layer type

The stationary Navier–Stokes system of equations is considered in a domain $\Omega \subset\mathbb R^3$ coinciding for large $|x|$ with the layer $\Pi =\mathbb R^2\times (0,1)$. A theorem is proved about the asymptotic behaviour of the solutions as $|x|\to\infty$. In particular, it is proved that for arbitrary data of the problem the solutions having non-zero flux through a cylindrical cross-section of the layer behave at infinity like the solutions of the linear Stokes system.