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Keywords:
existence; weak solutions; incompressible fluids; non-Newtonian fluids; pressure dependent viscosity; shear dependent viscosity; inflow/outflow boundary conditions; pressure boundary conditions; filtration boundary conditions
Summary:
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 inflow/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.
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