TY  - JOUR
ID  - 2008-15
T1  - On Pressure Boundary Conditions for Steady Flows of Incompressible Fluids with Pressure and Shear Rate Dependent Viscosities
A1  - Lanzendörfer, Martin
A1  - Stebel, Jan
JA  - Applications of Mathematics
Y1  - 2011
VL  - 56
IS  - 3
SP  - 265
EP  - 285
UR  - http://am.math.cas.cz/full/56/3/am56_3_2.pdf
M2  - doi: 10.1007/s10492-011-0016-1
KW  - existence of weak solutions
KW  - filtration boundary conditions
KW  - Incompressible fluids
KW  - inflow/outflow boundary conditions
KW  - non-Newtonian fluid
KW  - pressure boundary conditions
KW  - Pressure-dependent viscosity
KW  - shear-dependent viscosity
N2  - We consider a class of incompressible fluids whose viscosities depend on the pressure and the shear rate. Suitable boundary conditions on the traction at the in- flow/outflow part of boundary are given. As an advantage of this, the mean value of the pressure over the domain is no more a free parameter which would have to be prescribed otherwise. We prove the existence and uniqueness of weak solutions (the latter for small data) and discuss particular applications of the results.
ER  -