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

Kristina Kaulakyte

DOI: http://dx.doi.org/10.12775/TMNA.2015.070

Abstract


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.


Keywords


Navier-Stokes equations; nonhomogeneous boundary value problem; layer type outlet; nonzero flux

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