Partial regularity for the Navier-Stokes-Fourier system |
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Authors: | Luisa Consiglieri |
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Institution: | Independent Researcher, Painel da Lameira Cx 8, 7300-405 Portalegre, Portugal |
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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 conditions. 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. |
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Keywords: | partial regularity Navier-Stokes-Fourier system Joule effect suitable weak solutions |
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