On the existence of weak solutions to the equations of non-stationary motion of heat-conducting incompressible viscous fluids

This paper is concerned with the equations of non-stationary motion in 3D of heat-conducting incompressible viscous fluids with temperature-dependent viscosity. The conservation of internal energy includes the usual dissipation term. We prove the existence of a "weak solution with defect measure" to the system of PDEs under consideration. Our method of proof is based on a regularization of the equations of conservation of momentum.