In this paper, we investigate the convergence of the global large solution to its associated constant equilibrium state with an explicit decay rate for the compressible Navier–Stokes equations in three-dimensional whole space. Suppose the initial data belongs to some negative Sobolev space instead of Lebesgue space, we not only prove the negative Sobolev norms of the solution being preserved along time evolution, but also obtain the convergence of the global large solution to its associated constant equilibrium state with algebra decay rate. Besides, we shall show that the decay rate of the first order spatial derivative of large solution of the full compressible Navier–Stokes equations converging to zero in $L^2-$norm is ${(1+t)}^{-\frac{5}{4}}$, which coincides with the heat equation. This extends the previous decay rate ${(1+t)}^{-\frac{3}{4}}$ obtained in He et al. (2020).

在本文中，我们研究了全局大解对其相关恒定平衡状态的收敛性，并在三维全空间中研究了可压缩 Navier-Stokes 方程的显式衰减率。假设初始数据属于某个负 Sobolev 空间而不是 Lebesgue 空间，我们不仅证明了解的负 Sobolev 范数在时间演化过程中保持不变，而且通过代数得到全局大解与其相关的常平衡态的收敛性衰减率。此外，我们将证明完全可压缩 Navier-Stokes 方程的大解的一阶空间导数的衰减率在${升}^2-$规范是 ${(1+吨)}^{-\frac{5}{4}}$，与热方程一致。这扩展了之前的衰减率${(1+吨)}^{-\frac{3}{4}}$在 He 等人中获得。(2020)。