TY  - JOUR
ID  - 2007-29
T1  - On steady flows of incompressible fluids with implicit power-law-like rheology
A1  - Bulíček, Miroslav
A1  - Gwiazda, Piotr
A1  - Málek, Josef
A1  - Świerczewska-Gwiazda, Agnieszka
JA  - Advances in Calculus of Variations
Y1  - 2009
VL  - 2
IS  - 2
SP  - 109
EP  - 136
SN  - 1864-8258
N1  - Preprint no. 2007-29
UR  - http://www.karlin.mff.cuni.cz/ncmm/preprints/07309143420bgmsg061107.pdf
M2  - doi: 10.1515/ACV.2009.006
KW  - discontinuous viscosity
KW  - existence
KW  - implicit constitutive equation
KW  - Incompressible fluids
KW  - large data
KW  - Lipschitz approximations of Sobolev functions
KW  - Power-law fluids
KW  - weak solution
KW  - Young measures
N2  - We consider steady flows of incompressible fluids with power-law-like rheology given by an implicit constitutive equation relating the Cauchy stress and the symmetric part of the velocity gradient in such a way that it leads to a maximal monotone (possibly multivalued) graph. Such a framework includes standard Navier–Stokes and power-law fluids, Bingham fluids, Herschel–Bulkley fluids, and shear-rate dependent fluids with discontinuous viscosities as special cases. We assume that the fluid adheres to the boundary.

Using tools such as the Young measures, properties of spatially dependent maximal monotone operators and Lipschitz approximations of Sobolev functions, we are able to extend the results concerning large data existence of weak solutions to those values of the power-law index that are of importance from the point of view of engineering and physical applications.
M1  - fjournal={Advances in Calculus of Variations}
M1  - 
mrclass={35Q35 (35D05 76D03)}
M1  - 
mrnumber={MR2523124}
ER  -