  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 $\Pi=\frac{\text
{divdiv}}{-\Delta}(u_{i}u_{j})$ of the 3D incompressible Navier-Stokes
equations on bounded domain, we generalize Beirao da Veiga's result in [1] from
the incompressible Navier-Stokes equations to the isentropic compressible
Navier-Stokes system in the case away from vacuum.
