On pressure-driven Hele–Shaw flow of power-law fluids

References

• Marušić S, Marušić-Paloka E. Two-scale convergence for thin domains and its applications to some lower-dimensional models in fluid mechanics. Asymptot Anal. 2000;23(1):23–57.
   Web of Science ®Google Scholar
• Fabricius J, Miroshnikova E, Tsandzana A, et al. Pressure-driven flow in thin domains. Asymptot Anal. 2020;116(1):1–26.
   Web of Science ®Google Scholar
• Batchelor GK. An introduction to fluid dynamics. Cambridge: Cambridge University Press; 2000.
   Google Scholar
• Hele-Shaw HS. The flow of water. Nature. 1898;58:34–36.
   Google Scholar
• Huilgol RR. Fluid mechanics of viscoplasticity. Berlin: Springer; 2015.
   Google Scholar
• Davis AMJ, Mai T-Z. Steady pressure-driven non-Newtonian flow in a partially filled pipe. J Non-Newton Fluid Mech. 1991;41(1–2):81–100.
   Web of Science ®Google Scholar
• Jang HK, Hong SO, Lee SB, et al. Viscosity measurement of non-Newtonian fluids in pressure-driven flows of general geometries based on energy dissipation rate. J Non-Newton Fluid Mech. 2019;274(104204):00–00.
   Google Scholar
• Marušić-Paloka E. Mathematical modeling of junctions in fluid mechanics via two-scale convergence. J Math Anal Appl. 2019;480(1):25.
   Web of Science ®Google Scholar
• Pereira GG. Effect of variable slip boundary conditions on flows of pressure-driven non-Newtonian fluids. J Non-Newton Fluid Mech. 2009;157(3):197–206.
   Web of Science ®Google Scholar
• Aronsson G, Janfalk U. On Hele-Shaw flow of power-law fluids. European J Appl Math. 1992;3(4):343–366.
   Google Scholar
• Mikelić A, Tapiéro R. Mathematical derivation of the power law describing polymer flow through a thin slab. RAIRO-Modél Math Anal Numér.. 1995;29(1):3–21.
   Web of Science ®Google Scholar
• Gilbert RP, Fang M. An obstacle problem in non-isothermal and non-Newtonian Hele-Shaw flows. Commun Appl Anal. 2004;8(4):459–489.
   Google Scholar
• Nassehi V. Generalized Hele-Shaw models for non-Newtonian, non-isothermal flow in thin curved layers. IMA J Math Appl Bus Ind. 1996;7(1):71–88.
   Google Scholar
• Kondic L, Palffy-Muhoray P, Shelley M. Models of non-Newtonian Hele-Shaw flow. Phys Rev E. 1996;54(5):4536–4539.
   Web of Science ®Google Scholar
• Paşa G. Some non-Newtonian effects in Hele-Shaw displacements. Rev Roumaine Math Pured Appl. 2016;61(4):293–304.
   Web of Science ®Google Scholar
• Reynolds O. On the theory of lubrication and its application to Mr. Beauchamp Tower's experiments. Phil Trans Roy Soc London. 1886;177:157–234.
   Google Scholar
• Panton RL. Incompressible flow. 4th ed. Hoboken: Wiley; 2013.
   Google Scholar
• Bayada G, Chambat M. The transition between the Stokes equations and the Reynolds equation: a mathematical proof. Appl Math Optim. 1986;14(1):73–93.
   Web of Science ®Google Scholar
• Bayada G, Boukrouche M, El-A. Talibi M. The transient lubrication problem as a generalized Hele-Shaw type problem. Z Anal Anwend. 1995;14(1):59–87.
   Google Scholar
• Anguiano M, Suárez-Grau FJ. Nonlinear Reynolds equations for non-Newtonian thin-film fluid flows over a rough boundary. IMA J Appl Math. 2019;84(1):63–95.
   Web of Science ®Google Scholar
• Anguiano M, Suárez-Grau FJ. Homogenization of an incompressible non-Newtonian flow through a thin porous medium. Z Angew Math Phys. 2017;68(2):25.
   Web of Science ®Google Scholar
• Geymonat G, Suquet P. Functional spaces for Norton-Hoff materials. Math Meth Appl Sci. 1986;8(2):206–222.
   Google Scholar
• Boyer F, Fabrie P. Mathematical tools for the study of the incompressible Navier-Stokes equation and related models. New York: Springer; 2013.
   Google Scholar
• Fabricius J. Stokes flow with kinematic and dynamic boundary conditions. Quart Appl Math. 2019;77(3):525–544.
   Web of Science ®Google Scholar
• Zeidler E. Nonlinear functional analysis and its applications II/B. New York: Springer; 1990.
   Google Scholar
• Bogovski ME. Solution of the first boundary value problem for the equation of continuity of an incompressible medium. Dokl Akad Nauk SSSR. 1979;248(5):1037–1040.
   Google Scholar
• Nečas J. Direct methods in the theory of elliptic equations. New York: Springer; 2012.
   Google Scholar
• Tartar L. Topics in nonlinear analysis. Orsay: Publications Mathématiques d'Orsay, Université de Paris-Sud; 1978.
   Google Scholar
• Barnes HA, Hutton JF, Walters K. An introduction to rheology. Amsterdam: Elsevier; 1989.
   Google Scholar
• Astarita G, Marrucci G. Principles of non-Newtonian fluid mechanics. Maidenhead: McGraw-Hill; 1974.
   Google Scholar
• Grisvard P. Elliptic problems in nonsmooth domains. Boston (MA): Pitman; 1985.
   Google Scholar
• Lindqvist P. On the equation div (|∇u|p−2∇u)+λ|u|p−2u=0. Proc Amer Math Soc. 1990;109(1):157–164.
   Web of Science ®Google Scholar
• Brezis H. Analyse fonctionnelle - Théorie et applications. Paris: Masson; 1983.
   Google Scholar