On the Navier-Stokes equations with temperature-dependent transport coefficients - Eduard Feireisl; Josef Málek (Differential Equations and Nonlinear Mechanics)
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.