Journal of Mathematical Fluid Mechanics

, Volume 17, Issue 3, pp 495–511 | Cite as

Global Solvability of the One-Dimensional Cosserat–Bingham Fluid Equations

  • V.V. Shelukhin
  • N.V. ChemetovEmail author


The equations for micropolar Bingham fluid are considered and global existence of a weak solution for pressure driven flows is proved for a one-dimensional boundary-value problem with periodic boundary conditions. In contrast to the classical Bingham fluid, the micropolar Bingham fluid supports local micro-rotations and two types of plug zones. Our approach is different from that of Duvaut–Lions developed for the classical Bingham viscoplastic materials. We do not apply the variational inequality but make use an approximation of the generalized Bingham fluid by a Non-Newtonian fluid with a continuous constitutive law.


Micropolar viscoplastic fluid yield stress non-Newtonian fluid approximation global existence 


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© Springer Basel 2015

Authors and Affiliations

  1. 1.Siberian Division of Russian Academy of SciencesNovosibirsk State University, Lavrentyev Institute of HydrodynamicsNovosibirskRussia
  2. 2.CMAF-CIO/Universidade de LisboaLisbonPortugal

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