SIAM Journal on Mathematical Analysis, Volume 52, Issue 2, Page 1363-1385, January 2020.
We study the energy balance for the weak solutions of the three-dimensional compressible Navier--Stokes equations in a bounded domain. By constructing a global mollification combined with an independent boundary cut-off and then taking a double limit to prove the convergence of the resolved energy, we establish an $L^{p}$-$L^{q}$ regularity condition on the velocity field for the energy equality to hold, provided that the density is bounded and satisfies $\sqrt{\rho} \in L^\infty_t H^1_x$. As a result of our new approach, we can avoid assuming additional regularity of the velocity near the boundary in order to deal with the boundary production due to the diffusion terms.

中文翻译：

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具有物理边界的可压缩流体的能量均等

SIAM数学分析杂志，第52卷，第2期，第1363-1385页，2020年1月。
我们研究了有界域中三维可压缩Navier-Stokes方程的弱解的能量平衡。通过构造结合独立边界截止的全局旋转，然后采用双重限制来证明解析能量的收敛，我们在方程组上建立了一个$ L ^ {p} $-$ L ^ {q} $正则条件如果密度有界且满足$ \ sqrt {\ rho} \ in L ^ \ infty_t H ^ 1_x $，则保持能量相等的速度场。作为我们新方法的结果，我们可以避免假设边界附近的速度具有其他规律性，以便处理由于扩散项引起的边界产生。