Homogenization of the Stokes equations with a random potential

abstract

• Homogenization of the Stokes equations in a random porous medium is considered. Instead of the homogeneous Dirichlet condition on the boundaries of numerous small pores, used in the existing work on the subject, we insert a term with a positive rapidly oscillating potential into the equations. Physically, this corresponds to porous media whose rigid matrix is slightly permeable to fluid. This relaxation of the boundary value problem permits one to study the asymptotics of the solutions and to justify the Darcy law for the limit functions under much fewer restrictions. Specifically, homogenization becomes possible without any connectedness conditions for the porous domain, whose verification would lead to problems of percolation theory that are insufficiently studied. 1996 Plenum Publishing Corporation.

authors

• Efendiev, Yalchin

published proceedings

• MATHEMATICAL NOTES

author list (cited authors)

• Belyaev, A. Y., & Efendiev, Y. R.

citation count

• 2

complete list of authors

• Belyaev, AY||Efendiev, YR

publication date

• April 1996

publisher

• Springer Nature  Publisher

published in

• Mathematical Notes  Journal

keywords

• 49 Mathematical Sciences
• 4901 Applied Mathematics

Digital Object Identifier (DOI)

• 10.1007/BF02308685

start page

• 361

end page

• 372

volume

• 59

issue

• 3-4

URL

• http://dx.doi.org/10.1007/bf02308685