Partial regularity for the Navier-Stokes-Fourier system

Details Partial regularity for the Navier-Stokes-Fourier system Partial regularity for the Navier-Stokes-Fourier system

2009-10-24

arxiv.org/abs/0910.4654v2

Acta Mathematica Scientia vol. 31B n. 5 (2011), 1653-1670

Mathematics

Analysis of PDEs

25 pages, v2: Navier/Dirichlet boundary conditions replace homogeneous Dirichlet boundary conditions

Scientific paper

10.1016/S0252-9602(11)60351-2

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 to 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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