On Nonhomogeneous Boundary Value Problem for the Steady Navier-Stokes System in Domain with Paraboloidal and Layer Type Outlets to Infinity
DOI:
https://doi.org/10.12775/TMNA.2015.070Keywords
Navier-Stokes equations, nonhomogeneous boundary value problem, layer type outlet, nonzero fluxAbstract
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 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.
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