### Abstract

We assume that Ω is a domain in ℝ ^{2} or in ℝ ^{3} with a non-compact boundary, representing a generally inhomogeneous and anisotropic porous medium. We prove the weak solvability of the boundary-value problem, describing the steady motion of a viscous incompressible fluid in Ω. We impose no restriction on sizes of the velocity fluxes through unbounded components of the boundary of Ω. The proof is based on the construction of appropriate Galerkin approximations and study of their convergence. In Sect. 4, we provide several examples of concrete forms of Ω and prescribed velocity profiles on ∂Ω, when our main theorem can be applied.

Original language | English |
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Pages (from-to) | 23-42 |

Number of pages | 20 |

Journal | Acta Applicandae Mathematicae |

Volume | 119 |

Issue number | 1 |

DOIs | |

Publication status | Published - Jun 1 2012 |

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### All Science Journal Classification (ASJC) codes

- Applied Mathematics

### Cite this

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*Acta Applicandae Mathematicae*, vol. 119, no. 1, pp. 23-42. https://doi.org/10.1007/s10440-011-9659-x

**A steady weak solution of the equations of motion of a viscous incompressible fluid through porous media in a domain with a non-compact boundary.** / Akyildiz, Fahir Talay; Neustupa, Jiří; Siginer, Dennis.

Research output: Contribution to journal › Article

TY - JOUR

T1 - A steady weak solution of the equations of motion of a viscous incompressible fluid through porous media in a domain with a non-compact boundary

AU - Akyildiz, Fahir Talay

AU - Neustupa, Jiří

AU - Siginer, Dennis

PY - 2012/6/1

Y1 - 2012/6/1

N2 - We assume that Ω is a domain in ℝ 2 or in ℝ 3 with a non-compact boundary, representing a generally inhomogeneous and anisotropic porous medium. We prove the weak solvability of the boundary-value problem, describing the steady motion of a viscous incompressible fluid in Ω. We impose no restriction on sizes of the velocity fluxes through unbounded components of the boundary of Ω. The proof is based on the construction of appropriate Galerkin approximations and study of their convergence. In Sect. 4, we provide several examples of concrete forms of Ω and prescribed velocity profiles on ∂Ω, when our main theorem can be applied.

AB - We assume that Ω is a domain in ℝ 2 or in ℝ 3 with a non-compact boundary, representing a generally inhomogeneous and anisotropic porous medium. We prove the weak solvability of the boundary-value problem, describing the steady motion of a viscous incompressible fluid in Ω. We impose no restriction on sizes of the velocity fluxes through unbounded components of the boundary of Ω. The proof is based on the construction of appropriate Galerkin approximations and study of their convergence. In Sect. 4, we provide several examples of concrete forms of Ω and prescribed velocity profiles on ∂Ω, when our main theorem can be applied.

UR - http://www.scopus.com/inward/record.url?scp=84860683265&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84860683265&partnerID=8YFLogxK

U2 - 10.1007/s10440-011-9659-x

DO - 10.1007/s10440-011-9659-x

M3 - Article

VL - 119

SP - 23

EP - 42

JO - Acta Applicandae Mathematicae

JF - Acta Applicandae Mathematicae

SN - 0167-8019

IS - 1

ER -