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HERSCHEL–BULKLEY FLUIDS: EXISTENCE AND REGULARITY OF STEADY FLOWS

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- ERRATUM: "HERSCHEL–BULKLEY FLUIDS: EXISTENCE AND REGULARITY OF STEADY FLOWS"

Charles University, Faculty of Mathematics and Physics, Mathematical Institute, Sokolovská 83, 18675 Prague 8, Czech Republic

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M. RŮŽIČKA

Mathematical Institute, Section of Applied Mathematics, Albert–Ludwigs–University Freiburg, Eckerstr. 1, D–79104 Freiburg, Germany

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, and

V. V. SHELUKHIN

Lavrentyev Institute of Hydrodynamics, Siberian Division of Russian Academy of Sciences, Lavrentyev pr. 15, Novosibirsk 630090, Russia

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https://doi.org/10.1142/S0218202505000996Cited by:36 (Source: Crossref)

Abstract

The equations for steady flows of Herschel–Bulkley fluids are considered and the existence of a weak solution is proved for the Dirichlet boundary-value problem. The rheology of such a fluid is defined by a yield stress τ* and a discontinuous constitutive relation between the Cauchy stress and the symmetric part of the velocity gradient. Such a fluid stiffens if its local stresses do not exceed τ*, and it behaves like a non-Newtonian fluid otherwise. We address here a class of nonlinear fluids which includes shear-thinning p-law fluids with 9/5 < p ≤ 2. The flow equations are formulated in the stress-velocity setting (cf. Ref. 25). Our approach is different from that of Duvaut–Lions (cf. Ref. 10) developed for classical Bingham visco-plastic materials. We do not apply the variational inequality but make use of an approximation of the Herschel–Bulkley fluid with a generalized Newtonian fluid with a continuous constitutive law.

Keywords:

AMSC: 76A05, 74D10

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