Refined blow-up criteria for the full compressible Navier-Stokes equations involving temperature

In this paper, inspired by the study of the energy flux in local energy inequality of the 3D incompressible Navier-Stokes equations, we improve almost all the blow-up criteria involving temperature to allow the temperature in its scaling invariant space for the 3D full compressible Navier-Stokes equations. Enlightening regular criteria via pressure Pi = divdiv/-Delta (u(i) u(j)) of the 3D incompressible Navier-Stokes equations on bounded domain, we generalize Beirao da Veiga's result in (Chin Ann Math Ser B 16:407-412, 1995) from the incompressible Navier-Stokes equations to the isentropic compressible Navier-Stokes system in the case away from vacuum.