TY  - JOUR
T1  - On power-law fluids with the power-law index proportional to the pressure
A1  - Málek, Josef
A1  - Rajagopal, K. R.
A1  - Žabenský, Josef
JA  - Applied Mathematics Letters
Y1  - 2016
VL  - 62
SP  - 118
EP  - 123
M2  - doi: 10.1016/j.aml.2016.07.007
N2  - In this short note we study special unsteady flows of a fluid whose viscosity depends
on both the pressure and the shear rate. Here we consider an interesting dependence
of the viscosity on the pressure and the shear rate; a power-law of the shear rate
wherein the exponent depends on the pressure. The problem is important from
the perspective of fluid dynamics in that we obtain solutions to a technologically
relevant problem, and also from the point of view of mathematics as the analysis
of the problem rests on the theory of spaces with variable exponents. We use the
theory to prove the existence of solutions to generalizations of Stokes’ first and
second problem.
M1  - Preprint project = MORE
M1  - Preprint year = 2016
M1  - Preprint number = 37
M1  - Preprint ID = MORE/2016/37
ER  -