Abstract
The paper deals with the non-stationary Oseen system of equations for the generalized Newtonian incompressible fluid with multivalued and nonmonotone frictional slip boundary conditions. First, we provide a result on existence of a unique solution to an abstract evolutionary inclusion involving the Clarke subdifferential term for a nonconvex function. We employ a method based on a surjectivity theorem for multivalued L-pseudomonotone operators. Then, we exploit the abstract result to prove the weak unique solvability of the Oseen system.
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Communicated by Stefan Turek.
Research supported in part by the National Science Center of Poland under the Maestro Project No. DEC-2012/06/A/ST1/00262, and the International Project co-financed by the Ministry of Science and Higher Education of Republic of Poland under Grant No. 3792/GGPJ/H2020/2017/0.
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Migórski, S., Dudek, S. Evolutionary Oseen Model for Generalized Newtonian Fluid with Multivalued Nonmonotone Friction Law. J. Math. Fluid Mech. 20, 1317–1333 (2018). https://doi.org/10.1007/s00021-018-0367-4
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DOI: https://doi.org/10.1007/s00021-018-0367-4