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

Martin Lanzendörfer; Jan Stebel

Applications of Mathematics (2011)

  • Volume: 56, Issue: 3, page 265-285
  • ISSN: 0862-7940

Abstract

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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.

How to cite

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Lanzendörfer, Martin, and Stebel, Jan. "On pressure boundary conditions for steady flows of incompressible fluids with pressure and shear rate dependent viscosities." Applications of Mathematics 56.3 (2011): 265-285. <http://eudml.org/doc/116524>.

@article{Lanzendörfer2011,
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.},
author = {Lanzendörfer, Martin, Stebel, Jan},
journal = {Applications of Mathematics},
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; weak solution; incompressible fluid; non-Newtonian fluid; pressure dependent viscosity; shear dependent viscosity; inflow/outflow boundary conditions; pressure boundary condition; filtration boundary condition},
language = {eng},
number = {3},
pages = {265-285},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On pressure boundary conditions for steady flows of incompressible fluids with pressure and shear rate dependent viscosities},
url = {http://eudml.org/doc/116524},
volume = {56},
year = {2011},
}

TY - JOUR
AU - Lanzendörfer, Martin
AU - Stebel, Jan
TI - On pressure boundary conditions for steady flows of incompressible fluids with pressure and shear rate dependent viscosities
JO - Applications of Mathematics
PY - 2011
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 56
IS - 3
SP - 265
EP - 285
AB - 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.
LA - eng
KW - existence; weak solutions; incompressible fluids; non-Newtonian fluids; pressure dependent viscosity; shear dependent viscosity; inflow/outflow boundary conditions; pressure boundary conditions; filtration boundary conditions; weak solution; incompressible fluid; non-Newtonian fluid; pressure dependent viscosity; shear dependent viscosity; inflow/outflow boundary conditions; pressure boundary condition; filtration boundary condition
UR - http://eudml.org/doc/116524
ER -

References

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