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Stationary flow of non-Newtonian fluid with nonmonotone frictional boundary conditions

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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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Authors and Affiliations

  1. Faculty of Physics, Mathematics and Computer Science, Institute of Mathematics, Krakow University of Technology, ul. Warszawska 24, 31155, Kraków, Poland

    Sylwia Dudek

  2. Faculty of Mathematics and Computer Science, Jagiellonian University, ul. Stanisława Łojasiewicza 6, 30348, Kraków, Poland

    Piotr Kalita

  3. Institute of Mathematics, Lodz University of Technology, ul. Wolczanska 215, 90924, Lodz, Poland

    Stanisław Migórski

Authors
  1. Sylwia Dudek
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  2. Piotr Kalita
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  3. Stanisław Migórski
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Correspondence to Stanisław Migórski.

Additional information

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

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