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

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.