[1]	E. Feireisl, J. Neustupa, and J. Stebel. Convergence of a Brinkman-type penalization for compressible fluid flows. Preprint 13, Nečas Center for Mathematical Modeling, 2010. Submitted to J. Differential Equations. [ bib \| .pdf ] We show convergence of a Brinkman-type penalization of the com- pressible Navier-Stokes equation. In particular, the existence of weak solutions for the system in domains with boundaries varying in time is established.
[2]	J. Stebel. On shape stability of incompressible fluids subject to Navier's slip. Preprint 10, Nečas Center for Mathematical Modeling, 2010. Submitted to J. Math. Fluid Mech. [ bib \| .pdf ] The paper is concerned with the equations of motion for incompressible fluids that slip at the wall. Particular interest is in the domain dependence of weak solutions. We prove that the solutions depend continuously on the perturbation of the boundary provided that the latter remains in the class C^1,1. The result is applicable to a wide class of shape optimization problems and is optimal in terms of boundary regularity.
[3]	M. Lanzendörfer and J. Stebel. On a mathematical model of journal bearing lubrication. Preprint 206, Institute of Mathematics of the Academy of Sciences of the Czech Republic, 2010. Submitted to Mathematics and Computers in Simulation. [ bib \| .pdf ] We consider the steady motion of an incompressible fluid whose viscosity depends on the pressure and the shear rate. The system is completed by suitable boundary conditions involving non-homogeneous Dirichlet, Navier's slip and inflow/outflow parts. We prove the existence of weak solutions and show that the resulting level of the pressure is fixed by the boundary conditions. The problem is motivated by particular applications from tribology.
[4]	J. Haslinger and J. Stebel. Shape optimization for Navier-Stokes equations with algebraic turbulence model: Numerical analysis and computation. Preprint 26, Nečas Center for Mathematical Modeling, 2009. Submitted to Appl. Math. Optim. [ bib \| .pdf ] We study the 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 the optimal control problem in which the control variable is the shape of the domain representing the header, the state problem is represented by the generalized Navier-Stokes system with nontrivial boundary conditions. This paper deals with numerical aspects of the problem.
[5]	M. Lanzendörfer and J. Stebel. On Pressure Boundary Conditions for Steady Flows of Incompressible Fluids with Pressure and Shear Rate Dependent Viscosities. Preprint 15, Nečas Center for Mathematical Modeling, 2008. To appear in Appl. Math. [ bib \| .pdf ] 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.