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pressure dependent viscosity; implicit constitutive theory; Poiseuille flow

References:

[1] G. G. Stokes: **On the theories of the internal friction of fluids in motion and of the equilibrium motion of elastic solids**. Trans. Cambridge Phil. Soc. 8 (1845), 287–305.

[2] P. W. Bridgman: **The Physics of High Pressure**. The MacMillan Company, New York, 1931.

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[4] W. G. Cutler, R. H. McMickle, W. Webb, and R. W. Schiessler: **Study of the compressions of several high molecular weight hydrocarbons**. J. Chem. Phys. 29 (1958), 727–740.

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[10] A. Z. Szeri: **Fluid Film Lubrication: Theory and Design**. Cambridge University Press, Cambridge, 1998. Zbl 1001.76001

[11] J. Hron, J. Málek, and K. R. Rajagopal: **Simple flows of fluids with pressure dependent viscosities**. Proc. R. Soc. Lond., Ser. A 457 (2001), 1603–1622. DOI 10.1098/rspa.2000.0723

[12] J. Málek, J. Nečas and K. R. Rajagopal: **Global analysis of the flows of fluid with pressure-dependent viscosities**. Arch. Ration. Mech. Anal. 165 (2002), 243–267. DOI 10.1007/s00205-002-0219-4 | MR 1941479

[13] E. L. Ince: **Ordinary Differential Equations**. Dover Publications, New York, 1944. MR 0010757 | Zbl 0063.02971

[14] N. W. McLachlan: **Bessel Functions for Engineers**. Clarendon Press, Oxford, 1955.

[15] A. Malewsky, D. Yen: **Strongly chaotic non-Newtonian mantle convection in the Earth’s mantle**. Geophys. Astrophys. Fluid Dynamics 65 (1996), 149–171.