## Topological Methods in Nonlinear Analysis

### On nonhomogeneous boundary value problem for the steady Navier-Stokes system in domain with paraboloidal and layer type outlets to infinity

Kristina Kaulakytė

#### 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.

#### Article information

Source
Topol. Methods Nonlinear Anal., Volume 46, Number 2 (2015), 835-865.

Dates
First available in Project Euclid: 21 March 2016

https://projecteuclid.org/euclid.tmna/1458588665

Digital Object Identifier
doi:10.12775/TMNA.2015.070

Mathematical Reviews number (MathSciNet)
MR3494974

Zentralblatt MATH identifier
1362.35211

#### Citation

Kaulakytė, Kristina. On nonhomogeneous boundary value problem for the steady Navier-Stokes system in domain with paraboloidal and layer type outlets to infinity. Topol. Methods Nonlinear Anal. 46 (2015), no. 2, 835--865. doi:10.12775/TMNA.2015.070. https://projecteuclid.org/euclid.tmna/1458588665

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