Applications of Mathematics

, Volume 56, Issue 3, pp 265–285

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


DOI: 10.1007/s10492-011-0016-1

Cite this article as:
Lanzendörfer, M. & Stebel, J. Appl Math (2011) 56: 265. doi:10.1007/s10492-011-0016-1


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 

Copyright information

© Institute of Mathematics of the Academy of Sciences of the Czech Republic, Praha, Czech Republic 2011

Authors and Affiliations

  1. 1.PrahaCzech Republic
  2. 2.Institute of Computer ScienceAcademy of Sciences of the Czech RepublicPraha 8Czech Republic
  3. 3.Institute of MathematicsAcademy of Sciences of the Czech RepublicPraha 1Czech Republic

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