This paper concerns the energy conservation for the weak solutions of the compressible Navier–Stokes equations. Assume that the density is positively bounded, we work on the regularity assumption on the gradient of the velocity, and establish a Lp–Ls type condition for the energy equality to hold in the distributional sense in time. We mention that no regularity assumption on the density derivative is needed any more.

中文翻译：

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可压缩 Navier-Stokes 方程能量守恒的正则判据

本文关注可压缩 Navier-Stokes 方程的弱解的能量守恒。假设密度是正有界的，我们对速度梯度进行规律性假设，并建立一个大号p–大号s能量等式在时间分布意义上保持的类型条件。我们提到不再需要对密度导数进行规律性假设。