Abstract
We study the stationary two-dimensional incompressible flow of non-Newtonian fluid governed by a nonlinear constitutive law and with a multivalued nonmonotone subdifferential frictional boundary condition. We provide an abstract result on existence of solution to an operator inclusion modeling the flow phenomenon. We prove a theorem on existence and, under additional assumptions, also uniqueness of weak solution to the flow problem.
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Research supported by the Marie Curie International Research Staff Exchange Scheme Fellowship within the 7th European Community Framework Programme under Grant Agreement No. 295118, the National Science Center of Poland under the Maestro Advanced 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. W111/7.PR/2012.
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Dudek, S., Kalita, P. & Migórski, S. Stationary flow of non-Newtonian fluid with nonmonotone frictional boundary conditions. Z. Angew. Math. Phys. 66, 2625–2646 (2015). https://doi.org/10.1007/s00033-015-0545-7
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DOI: https://doi.org/10.1007/s00033-015-0545-7