On pressure boundary conditions for steady flows of incompressible fluids with pressure and shear rate dependent viscosities

Abstract

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.

Keywords

• existence of weak solutions
• incompressible fluids
• non-Newtonian fluids
• pressure dependent viscosity
• shear dependent viscosity
• inflow/outflow boundary conditions
• pressure boundary conditions
• filtration boundary conditions