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 (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.

在本文中，受3D不可压缩Navier–Stokes方程在局部能量不等式中的能量通量研究的启发，我们改进了几乎所有涉及温度的爆炸准则，以允许温度在其3D完全可压缩的尺度不变空间中Navier–Stokes方程。通过有界域上的3D不可压缩Navier–Stokes方程的压力\（\ Pi = \ frac {\ text {divdiv}} {-\ Delta}（u_ {i} u_ {j}）\）启发常规准则，我们进行了概括Beirao da Veiga的结果（Chin Ann Math Ser B 16：407–412，1995）从不可压缩的Navier–Stokes方程到等熵可压缩的Navier–Stokes系统（在远离真空的情况下）。