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

0374149 - MÚ 2013 RIV NL eng J - Journal Article
Akyildiz, F.T. - Neustupa, Jiří - Siginer, D.
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.
Acta Applicandae Mathematicae. Roč. 119, č. 1 (2012), s. 23-42. ISSN 0167-8019. E-ISSN 1572-9036
R&D Projects: GA AV ČR IAA100190905
Institutional research plan: CEZ:AV0Z10190503
Keywords : flows in porous media * steady-state problems * inhomogeneous boundary data
Subject RIV: BA - General Mathematics
Impact factor: 0.985, year: 2012
http://www.springerlink.com/content/t8n71p67w2282t96/

We assume that Ω is a domain in 2 or in 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.
Permanent Link: http://hdl.handle.net/11104/0207133