On pressure boundary conditions for steady flows of incompressible fluids with pressure and shear rate dependent viscosities
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- Lanzendörfer, M. & Stebel, J. Appl Math (2011) 56: 265. doi:10.1007/s10492-011-0016-1
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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.