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

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Abstract

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.

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Authors and Affiliations

  1. Dipartimento di Matematica e Fisica, Università degli Studi della Campania “L. Vanvitelli”, viale Lincoln, 81100, Caserta, Italy

    Anna Abbatiello

  2. Faculty of Mathematics and Physics, Mathematical Institute, Charles University, Sokolovská 83, 186 75, Prague, Czech Republic

    Miroslav Bulíček

  3. Faculty of Mathematics and Physics, Department of Mathematical Analysis, Charles University, Sokolovská 83, 186 75, Prague, Czech Republic

    Petr Kaplický

Authors
  1. Anna Abbatiello
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  2. Miroslav Bulíček
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  3. Petr Kaplický
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Correspondence to Miroslav Bulíček.

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Communicated by E. Feireisl

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Anna Abbatiello is partially supported by National Group of Mathematical Physics (GNFM-INdAM) via GNFM Progetto Giovani 2017. Anna Abbatiello is also grateful to Charles University for the hospitality during her visit when the work was performed. Miroslav Bulíček’s work was supported by the Czech Science Foundation (Grant No. 16-03230S). Miroslav Bulíček and Petr Kaplický are members of Nečas Center for Mathematical Modeling.

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Abbatiello, A., Bulíček, M. & Kaplický, P. On the Existence of Classical Solution to the Steady Flows of Generalized Newtonian Fluid with Concentration Dependent Power-Law Index. J. Math. Fluid Mech. 21, 15 (2019). https://doi.org/10.1007/s00021-019-0415-8

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