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A. Abbatiello, M. Bulicek, E. Maringova:
"On the dynamic slip boundary condition for Navier-Stokes-like problems";
in: "ASC Report 35/2020", issued by: Institute for Analysis and Scientific Computing; Vienna University of Technology, Wien, 2020, ISBN: 978-3-902627-13-1, 1 - 37.

The choice of the boundary conditions in mechanical problems has to reflect the interaction of the considered material with the surface, despite the assumption of the no-slip condition is preferred to avoid boundary terms in the analysis and slipping effects are usually overlooked. Besides the "static slip models", there are phenomena not accurately described by them, e.g. in the moment when the slip changes rapidly, the wall shear stress and the slip can exhibit a sudden overshoot and subsequent relaxation. When these effects become signif-
icant, the so-called dynamic slip phenomenon occurs. We develop a mathematical analysis of Navier-Stokes-like problems with dynamic slip boundary condition, which requires a proper generalisation of the Gelfand triplet and the corresponding function spaces setting.

dynamic slip, weak solution, large data, existence, implicit constitutive theory.

http://www.asc.tuwien.ac.at/preprint/2020/asc35x2020.pdf