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@techreport{fenest_brinkman,
  title = {Convergence of a {B}rinkman-type penalization for compressible fluid flows},
  author = {E. Feireisl and J. Neustupa and J. Stebel},
  institution = {Ne{\v c}as Center for Mathematical Modeling},
  year = {2010},
  number = {13},
  type = {Preprint},
  abstract = {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.},
  url = {http://ncmm.karlin.mff.cuni.cz/preprints/1042141323pr13.pdf},
  note = {Submitted to J. Differential Equations}
}

@techreport{stebel_shape_stability,
  title = {On shape stability of incompressible fluids subject to {N}avier's slip},
  author = {J. Stebel},
  institution = {Ne{\v c}as Center for Mathematical Modeling},
  year = {2010},
  number = {10},
  type = {Preprint},
  abstract = {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.},
  url = {http://ncmm.karlin.mff.cuni.cz/preprints/1031112021pr10.pdf},
  note = {Submitted to J. Math. Fluid Mech.}
}

@techreport{lanzendorfer_stebel2009mcs,
  title = {On a mathematical model of journal bearing lubrication},
  author = {Lanzend{\"o}rfer, M. and Stebel, J.},
  institution = {Institute of Mathematics of the Academy of Sciences of the Czech Republic},
  year = {2010},
  number = {206},
  type = {Preprint},
  abstract = {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.},
  url = {http://www.math.cas.cz/preprint/pre-206.pdf},
  note = {Submitted to Mathematics and Computers in Simulation}
}

@techreport{haslinger_stebel2009ncmm,
  title = {{Shape optimization for Navier-Stokes equations with algebraic turbulence model: Numerical analysis and computation}},
  author = {Haslinger, J. and Stebel, J.},
  institution = {Ne{\v c}as Center for Mathematical Modeling},
  year = {2009},
  number = {26},
  url = {http://ncmm.karlin.mff.cuni.cz/preprints/09140095919pr26.pdf},
  type = {Preprint},
  abstract = {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.},
  note = {Submitted to Appl. Math. Optim.}
}

@techreport{lanzendorfer2008ncmm,
  title = {{On Pressure Boundary Conditions for Steady Flows of Incompressible Fluids with Pressure and Shear Rate Dependent Viscosities}},
  author = {Lanzend\"orfer, M. and Stebel, J.},
  institution = {Ne{\v c}as Center for Mathematical Modeling},
  year = {2008},
  number = {15},
  url = {http://www.karlin.mff.cuni.cz/ncmm/preprints/08311085315OnPressBndrCond-submitMB.pdf},
  type = {Preprint},
  abstract = {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.},
  note = {To appear in Appl. Math.}
}