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On pressure boundary conditions for steady flows of incompressible fluids with pressure and shear rate dependent viscosities. (English) Zbl 1224.35347
Summary: 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.

MSC:
35Q35 PDEs in connection with fluid mechanics
35J65 Nonlinear boundary value problems for linear elliptic equations
76D03 Existence, uniqueness, and regularity theory for incompressible viscous fluids
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