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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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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DOI: https://doi.org/10.1007/s10492-011-0016-1
Keywords
- existence
- weak solutions
- incompressible fluids
- non-Newtonian fluids
- pressure dependent viscosity
- shear dependent viscosity
- inflow/outflow boundary conditions
- pressure boundary conditions
- filtration boundary conditions