Abstract
The nonhomogeneous boundary value problem for the steady Navier-Stokes system is studied in a domain $\Omega$ with two layer type and one paraboloidaloutlets to infinity. The boundary$\partial\Omega$ is multiply connected and consists ofthe outer boundary $S$ and the inner boundary $\Gamma$. The boundary value ${a}$ is assumed to have a compact support. The flux of ${a}$ over the inner boundary $\Gamma$is supposed to be sufficiently small. We do not impose any restrictions on fluxesof ${a}$ over the unbounded components of the outer boundary $S$. Theexistence of at least one weak solution is proved.
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