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The nonhomogeneous boundary value problem for the steady Navier-Stokes system is studied in a domain $\Omega$ with two layer type and one paraboloidal outlets to infinity. The boundary $\partial\Omega$ is multiply connected and consists of the 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 fluxes of ${a}$ over the unbounded components of the outer boundary $S$. The existence of at least one weak solution is proved.

On Nonhomogeneous Boundary Value Problem for the Steady Navier-StokesSystem in Domain with Paraboloidal and Layer Type Outlets to Infinity