Communications in Mathematical Sciences

Volume 16 (2018)

Number 1

Analysis of the effects of a fissure for a non-Newtonian fluid flow in a porous medium

Pages: 273 – 292



María Anguiano (Departamento de Análisis Matemático, Facultad de Matemáticas, Universidad de Sevilla, Spain)

Francisco Javier Suárez-Grau (Departamento de Ecuaciones Diferenciales y Análisis Numérico, Facultad de Matemáticas, Universidad de Sevilla, Spain)


We study the solution of a non-Newtonian flow in a porous medium which characteristic size of the pores $\varepsilon$ and containing a fissure of width $\eta_\varepsilon$. The flow is described by the incompressible Stokes system with a nonlinear viscosity, being a power of the shear rate (power law) of flow index $1 \lt r \lt + \infty$. We consider the limit when size of the pores tends to zero and we obtain different models depending on the magnitude $\eta_\varepsilon$ with respect to $\varepsilon$.


non-Newtonian flow, Stokes equation, Darcy’s law, porous medium, fissure

2010 Mathematics Subject Classification

35B27, 76M50

María Anguiano has been supported by Junta de Andalucía (Spain), Proyecto de Excelencia P12-FQM-2466. Francisco Javier Suárez-Grau has been supported by Ministerio de Economía y Competitividad (Spain), Proyecto Excelencia MTM2014-53309-P.

Received 23 April 2017

Accepted 22 November 2017

Published 29 March 2018