We consider a class of incompressible fluids whose viscosities depend on the pressure and the shear rate. Suitable boundary conditions on the surface force 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 the uniqueness of weak solutions (the later for small data) and discuss particular applications of the results.

We study a shape optimization problem for the paper machine headbox which distributes a mixture of water and wood fibers in the paper making process. The aim is to find a shape which a priori ensures the given velocity profile on the outlet part. The mathematical formulation leads to an optimal control problem in which the control variable is the shape of the domain representing the header, the state problem is represented by a generalized stationary Navier-Stokes system with nontrivial mixed boundary conditions. In this paper we prove the existence of solutions both to the generalized Navier-Stokes system and to the shape optimization problem.

We study a 2D model of the orientation distribution of fibres in a paper machine headbox. The goal is to control the orientation of fibres at the outlet by shape variations. The mathematical formulation leads to an optimization problem with control in coefficients of a linear convection-diffusion equation as the state problem. Existence of solutions both to the state and the optimization problem is analyzed and sensitivity analysis is performed. Further, discretization is done and a numerical example is shown.

We study a shape optimization problem for a paper machine headbox which distributes a mixture of water and wood fibers in the paper manufacturing process. The aim is to find a shape which a priori ensures the given velocity profile on the outlet part. The mathematical formulation leads to an optimal control problem in which the control variable is the shape of the domain representing the header, the state problem is represented by the generalised Navier-Stokes system with nontrivial boundary conditions. The objective of this paper is to prove the existence of an optimal shape.

We study a shape optimization problem for a paper machine headbox which distributes a mixture of water and wood fibers in the paper manufacturing process. The aim is to find a shape which a priori ensures the given velocity profile on the outlet part. The state problem is represented by the generalised Navier-Stokes system with nontrivial boundary conditions. The objective of this paper is to prove the existence of an optimal shape.