Journal of Mathematical Fluid Mechanics

, Volume 20, Issue 3, pp 1317–1333 | Cite as

Evolutionary Oseen Model for Generalized Newtonian Fluid with Multivalued Nonmonotone Friction Law

  • Stanisław Migórski
  • Sylwia Dudek
Open Access


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.


Oseen model generalized Newtonian fluid hemivariational inequality L-pseudomonotonicity Clarke subdifferential friction-type law slip boundary condition 

Mathematics Subject Classification

47J20 47J22 49J40 49J45 74G25 74G30 74M15 


Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interests.


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Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (, which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Authors and Affiliations

  1. 1.College of Applied MathematicsChengdu University of Information TechnologyChengduPeople’s Republic of China
  2. 2.Chair of Optimization and ControlJagiellonian University in KrakowKrakowPoland
  3. 3.Institute of Mathematics Faculty of Physics, Mathematics and Computer ScienceKrakow University of TechnologyKrakowPoland

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