On the Existence of Classical Solution to the Steady Flows of Generalized Newtonian Fluid with Concentration Dependent Power-Law Index

  • Anna Abbatiello
  • Miroslav BulíčekEmail author
  • Petr Kaplický


Steady flows of an incompressible homogeneous chemically reacting fluid are described by a coupled system, consisting of the generalized Navier–Stokes equations and convection–diffusion equation with diffusivity dependent on the concentration and the shear rate. Cauchy stress behaves like power-law fluid with the exponent depending on the concentration. We prove the existence of a classical solution for the two dimensional periodic case whenever the power law exponent is above one and less than infinity.


Synovial fluid \(C^{1, \alpha }\) regularity Generalized viscosity Variable exponent Steady p-Navier–Stokes system 

Mathematics Subject Classification

Primary: 35Q35 Secondary: 76Z05 (76D03, 76A05) 


Compliance with ethical standards

Conflict of interest

Authors declare that they have no conflict of interest.


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Authors and Affiliations

  1. 1.Dipartimento di Matematica e FisicaUniversità degli Studi della Campania “L. Vanvitelli”CasertaItaly
  2. 2.Faculty of Mathematics and Physics, Mathematical InstituteCharles UniversityPragueCzech Republic
  3. 3.Faculty of Mathematics and Physics, Department of Mathematical AnalysisCharles UniversityPragueCzech Republic

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