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

Differential Equations and Nonlinear Mechanics
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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.

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