Journal provides a multidisciplinary forum for scientists, researchers and engineers involved in research and design of nonlinear processes and phenomena, including the nonlinear modelling of phenomena of the nature.

In this paper, we study the nonhomogeneous 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 ( -type domain), one self-symmetric outlet ( -type domain) or two self-symmetric outlets ( -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.

The nonhomogeneous boundary value problem for the stationary NavierStokes equations in 2D symmetric multiply connected domain with a cusp point on the boundary is studied. It is assumed that there is a source or sink in the cusp point. A symmetric solenoidal extension of the boundary value satisfying the LerayHopf inequality is constructed. Using this extension, the nonhomogeneous boundary value problem is reduced to homogeneous one and the existence of at least one weak symmetric solution is proved. No restrictions are assumed on the size of fluxes of the boundary value. Keyword : stationary Navier–Stokes equations, nonhomogeneous boundary condition, cusp point singularity, multiply connected domain, nonzero fluxes