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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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