Applications of Mathematics

, Volume 56, Issue 3, pp 265-285

First online:

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

  • Martin LanzendörferAffiliated withInstitute of Computer Science, Academy of Sciences of the Czech Republic Email author 
  • , Jan StebelAffiliated withInstitute of Mathematics, Academy of Sciences of the Czech Republic

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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.


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

MSC 2010

35Q35 35J65 76D03