On nonhomogeneous boundary value problems for the stationary Navier–Stokes equations in two-dimensional symmetric semi-infinite outlets

Abstract

We study the stationary nonhomogeneous Navier–Stokes problem in a two-dimensional symmetric domain with a semi-infinite outlet (for instance, either paraboloidal or channel-like). Under the symmetry assumptions on the domain, boundary value and external force, we prove the existence of at least one weak symmetric solution without any restriction on the size of the fluxes, i.e. the fluxes of the boundary value [Formula: see text] over the inner and the outer boundaries may be arbitrarily large. Only the necessary compatibility condition (the total flux is equal to zero) has to be satisfied. Moreover, the Dirichlet integral of the solution can be finite or infinite depending on the geometry of the domain.