On the Navier-Stokes equations with temperature-dependent transport coefficientsReport as inadecuate

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Differential Equations and Nonlinear Mechanics - Volume 2006 2006, Article ID 90616, 14 pages

Mathematical Institute, Academy of Sciences of the Czech Republic, Žitná 25, Praha 1 115 67, Czech Republic

Mathematical Institute, Faculty of Mathematics and Physics, Charles University in Prague, Sokolovská 83, Praha 8 18675, Czech Republic

Received 13 September 2005; Revised 2 April 2006; Accepted 3 April 2006

Copyright © 2006 Eduard Feireisl and Josef Málek. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We establish long-time and large-data existence of a weak solutionto the problem describing three-dimensional unsteady flows of anincompressible fluid, where the viscosity and heat-conductivitycoefficients vary with the temperature. The approach reposes onconsidering the equation for the total energy rather than theequation for the temperature. We consider the spatially periodicproblem.

Author: Eduard Feireisl and Josef Málek

Source: https://www.hindawi.com/


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