Asymptotics of solutions to the Navier–Stokes system with nonzero flux in a layer-like domain

Abstract

The asymptotic behavior in a layer-like domain of weak solutions with nonzero fluxes for the Dirichlet problem of the stationary Navier–Stokes system is investigated. If the data decay sufficiently fast, then first three asymptotic terms of any solution which grows at infinity not “too fast” have the same structure as those for the linear Stokes problem. The first asymptotic term which occurs due to the nonlinearity is of order |x|⁻³ at infinity in the velocity part; it is constructed explicitly. The results are obtained without any assumption on the smallness of the data.