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

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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.

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Correspondence to Martin Lanzendörfer.

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Jan Stebel was supported by the Nečas Center for Mathematical Modelling project LC06052 financed by MŠMT. Martin Lanzendörfer acknowledges the support of Czech Science Foundation project GA201/06/0352.

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Lanzendörfer, M., Stebel, J. On pressure boundary conditions for steady flows of incompressible fluids with pressure and shear rate dependent viscosities. Appl Math 56, 265–285 (2011). https://doi.org/10.1007/s10492-011-0016-1

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