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  • European Journal of Applied Mathematics, Volume 3, Issue 4
  • December 1992, pp. 343-366

On Hele–Shaw flow of power-law fluids

  • Gunnar Aronsson (a1) and Ulf Janfalk (a1)
  • DOI:
  • Published online: 01 July 2009

This paper reviews the governing equations for a plane Hele–Shaw flow of a power-law fluid. We find two closely related partial differential equations, one for the pressure and one for the stream function. Some mathematical results for these equations are presented, in particular some exact solutions and a representation theorem. The results are applied to Hele–Shaw flow. It is then possible to determine the flow near an arbitrary corner for any power-law fluid. Other examples are also given.

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[Ar1]G. Aronsson 1986 Construction of singular solutions to the p–harmonic equation and its limit equation for p =∞. Manuscripta Math. 56, 135158.

[Ar2]G. Aronsson 1988 On certain p-harmonic functions in the plane. Manuscripta Math. 61, 79101.

[Ar3]G. Aronsson 1989 Representation of a p–harmonic function near a critical point in the plane. Manuscripta Math. 66, 7395.

[AL]G. Aronsson & P. Lindqvist 1988 On p–harmonic functions in the plane and their stream functions. J. Derential Equations 74, 157178.

[BHW]H. A. Barnes , J. F. Hutton & K. Walters 1989 An Introduction to Rheology. Elsevier.

[D]M. Dobrowolski 1985 On finite element methods for nonlinear elliptic problems in domains with corners. Lecture Notes in Mathematics 1121, 85103, Springer-Verlag.

[HL]O. Hassager & T. L. Lauridsen 1988 Singular behaviour of power-law fluids in Hele-Shaw flow. J. Non-Newt. Fluid Mech. 29, 337346.

[L1]J. Lewis 1977 Capacitary functions in convex rings. Arch. Rational Mech. Anal. 66, 201224.

[L2]J. Lewis 1983 Regularity of the derivatives of certain degenerate elliptic equations. Indiana Univ. Math. J. 32, 849858.

[M]J. J. Manfredi 1988 p–harmonic functions in the plane. Proc. Amer. Math. Soc. 103, 473479.

[T]P. Tolksdorf 1985 Invariance properties and special structures near conical boundary points. Lecture Notes in Mathematics, Vol. 1121, Springer-Verlag, 308318.

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European Journal of Applied Mathematics
  • ISSN: 0956-7925
  • EISSN: 1469-4425
  • URL: /core/journals/european-journal-of-applied-mathematics
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