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

Journal article

Authors / Editors

Siginer, Dennis

Research Areas

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Publication Details

Author list: Akyildiz FT, Neustupa J, Siginer D

Publisher: Springer

Place: DORDRECHT

Publication year: 2012

Journal: Acta Applicandae Mathematicae (0167-8019)

Journal acronym: ACTA APPL MATH

Volume number: 119

Issue number: 1

Start page: 23

End page: 42

Number of pages: 20

ISSN: 0167-8019

eISSN: 1572-9036

Languages: English-Great Britain (EN-GB)

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Abstract

We assume that Omega is a domain in a"e(2) or in a"e(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 Omega. We impose no restriction on sizes of the velocity fluxes through unbounded components of the boundary of Omega. 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 Omega and prescribed velocity profiles on a,Omega, when our main theorem can be applied.

Keywords

Flows in porous media, Inhomogeneous boundary data, Steady-state problems

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