In this paper, we revisit the optimal time decay rates of classical solutions to the 3D compressible Navier-Stokes equations. Based on a global priori estimate, the optimal time decay rates of the solution and its first order derivative in L²-norm are obtained if $H^l$-norm$(l\ge 4)$ of the initial perturbation around a constant state is small enough and $\parallel ({\rho }_0-\overline{\rho },m_0){\parallel }_{{\dot{B}}_{1,\infty }^{-s}}^{\ell }$ is bounded for $s\in [0,\frac{1}{2})$. Compared with the previous works by Hai-Liang Li and Ting Zhang (Math Meth Appl Sci 34:670-682, 2011), we remove the smallness of $\parallel ({\rho }_0-\overline{\rho },m_0){\parallel }_{{\dot{B}}_{1,\infty }^{-s}}$ and our condition involves only the low frequencies of the data in ${\dot{B}}_{1,\infty }^{-s}({\mathbb{R}}^3)$.

中文翻译：

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3D 可压缩 Navier-Stokes 方程经典解的最优衰减率

在本文中，我们重新审视了 3D 可压缩 Navier-Stokes 方程的经典解的最佳时间衰减率。基于全局先验估计，求解的最佳时间衰减率及其在L ^{2 -}范数中的一阶导数可通过以下方式获得：$H^{升}$-规范$(升\ge 4)$ 恒定状态周围的初始扰动足够小，并且 $\parallel ({\rho }_0-\overline{\rho },{米}_0){\parallel }_{{\dot{乙}}_{1,\infty }^{-秒}}^{\ell }$ 有界于 $秒\in [0,\frac{1}{2})$. 与 Hai-Liang Li 和 Ting Zhang 之前的作品 (Math Meth Appl Sci 34:670-682, 2011) 相比，我们去除了$\parallel ({\rho }_0-\overline{\rho },{米}_0){\parallel }_{{\dot{乙}}_{1,\infty }^{-秒}}$ 我们的条件只涉及数据的低频 ${\dot{乙}}_{1,\infty }^{-秒}({\mathbb{电阻}}^3)$.