关键词: partial regularity, Navier-Stokes-Fourier system, Joule effect, suitable weak solutions

Abstract:

This paper addresses a nonstationary flow of heat-conductive incompressible Newtonian fluid with temperature-dependent viscosity coupled with linear heat transfer with advection and a viscous heat source term, under Navier/Dirichlet boundary condi-tions. The partial regularity for the velocity of the fluid is proved for each proper weak solution, that is, for such weak solutions which satisfy some local energy estimates in a similar way to the suitable weak solutions of the Navier-Stokes system. Finally, we study the nature of the set of points in space and time upon which proper weak solutions could be singular.

Key words: partial regularity, Navier-Stokes-Fourier system, Joule effect, suitable weak solutions