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Journal of Mathematical Fluid Mechanics

, Volume 11, Issue 1, pp 110–125 | Cite as

On non-Newtonian Fluids with Energy Transfer

  • T. RoubíčekEmail author
Article

Abstract.

The model combining incompressible Navier–Stokes’ equation in a non-Newtonian p-power-law modification and the nonlinear heat equation is considered. Existence of its (very) weak solutions is proved for p > 11/5 under mild assumptions of the temperature-dependent stress tensor by careful successive limit passage in a Galerkin approximation.

Mathematics Subject Classification (2000).

35Q35 76A05 80A20 

Keywords.

Navier–Stokes equation heat equation enthalpy transformation very weak solution existence Galerkin approximation 

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Copyright information

© Birkhaueser 2007

Authors and Affiliations

  1. 1.Mathematical InstituteCharles UniversityPraha 8Czech Republic
  2. 2.Institute of Information Theory and AutomationAcademy of Sciences of the Czech RepublicPraha 8Czech Republic

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