We study the convergence to equilibrium for the full compressible Navier-Stokes equations on the torus ${\mathbb{T}}^3$. Under the conditions that both the density ρ and the temperature θ possess uniform in time positive lower and upper bounds, it is shown that global regular solutions converge to equilibrium with exponential rate. We improve the previous result obtained by Villani in (2009) [28] on two levels: weaker conditions on solutions and faster decay rates.

中文翻译：

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完全可压缩Navier-Stokes方程解的平衡收敛

我们研究圆环上全部可压缩Navier-Stokes方程的平衡收敛。 ${\mathbb{Ť}}^3$。在密度ρ和温度θ在时间上均具有正的上下边界的条件下，表明整体正则解以指数速率收敛到平衡。我们在两个级别上改进了Villani在（2009）[28]中获得的先前结果：较弱的解条件和较快的衰减率。