On the Navier-Stokes equations with temperature-dependent transport coefficients

Feireisl, Eduard; M&#225, Josef; lek

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Differential Equations and Nonlinear Mechanics
Volume 2006 (2006), Article ID 90616, 14 pages
doi:10.1155/DENM/2006/90616

On the Navier-Stokes equations with temperature-dependent transport coefficients

Eduard Feireisl¹ and Josef Málek²

¹Mathematical Institute, Academy of Sciences of the Czech Republic, Žitná 25, Praha 1 115 67, Czech Republic
²Mathematical 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.

Abstract

We establish long-time and large-data existence of a weak solution to the problem describing three-dimensional unsteady flows of an incompressible fluid, where the viscosity and heat-conductivity coefficients vary with the temperature. The approach reposes on considering the equation for the total energy rather than the equation for the temperature. We consider the spatially periodic problem.