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@ARTICLE{,
            author = {Bul{\'{\i}}{\v c}ek, Miroslav and M{\'{a}}lek, Josef},
             title = {Internal flows of incompressible fluids subject to stick-slip boundary conditions},
           journal = {Vietnam Journal of Mathematics},
            volume = {45},
              year = {2017},
             pages = {2017--220},
               doi = {10.1007/s10013-016-0221-z},
          abstract = {We study mathematical properties of internal three-dimensional flows of incompressible
heat-conducting fluids with stick-slip boundary conditions, which state that the
fluid adheres to the boundary until a certain criterion activates the slipping regime on the
boundary. We look at this type of activated boundary condition as at an implicit constitutive
equation on the boundary and establish the long-time and large-data existence of weak
solutions for the incompressible three-dimensional Navier–Stokes–Fourier system with the
viscosity and the heat conductivity depending on the temperature (internal energy). It is
essential for our approach to know that the pressure, i.e., the quantity that is a consequence
of the fact that the material is incompressible, is globally integrable. While this requirement
is in the case of unsteady flows subject to a no-slip boundary condition open for most
incompressible fluids, we show that this difficulty can be successfully overcome if one
replaces the no-slip boundary condition by a stick-slip boundary condition. The result relies
also on the approach developed in Bul´{\i}ˇcek et al. (Nonlinear Anal. Real World Appl. 10,
992–1015, 2009).},
  Preprint project = {MORE},
     Preprint year = {2015},
   Preprint number = {22},
       Preprint ID = {MORE/2015/22}
}