  In this paper we study the nonhomongeneous boundary value problem for the
stationary Navier-Stokes equations in two dimensional symmetric domains with
finitely many outlets to infinity. The domains may have no self-symmetric
outlet (V-type domain), one self-symmetric outlet (Y-type domain) or two
self-symmetric outlets (I-type domain). We construct a symmetric solenoidal
extension of the boundary value satisfying the Leray-Hopf inequality. After
having such an extension, the nonhomogeneous boundary value problem is reduced
to homogeneous one and the existence of at least one weak solution follows.
Notice that we do not impose any restrictions on the size of the fluxes over
the inner and outer boundaries. Moreover, the Dirichlet integral of the
solution can be either finite or infinite depending on the geometry of the
domains.

Analysis of PDEs