On solutions for a generalized Navier–Stokes–Fourier system fulfilling the entropy equality

  title={On solutions for a generalized Navier–Stokes–Fourier system fulfilling the entropy equality},
  author={Anna Abbatiello and Miroslav Bul{\'i}{\vc}ek and Petr Kaplick'y},
  journal={Philosophical transactions. Series A, Mathematical, physical, and engineering sciences},
We consider a flow of a non-Newtonian heat conducting incompressible fluid in a bounded domain subjected to the homogeneous Dirichlet boundary condition for the velocity field and the Dirichlet boundary condition for the temperature. In three dimensions, for a power-law index greater or equal to 11/5, we show the existence of a solution fulfilling the entropy equality. The entropy equality can be formally deduced from the energy equality by renormalization. However, such a procedure can be… 

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