Motivated by Lu and Zhang (J Differ Equ 376:406–468, 2023), we prove the global existence of solutions to the three-dimensional isentropic compressible Navier–Stokes equations with smooth initial data slowly varying in two directions. In such a setting, the \(L^2\)-norms of the initial data are of order \(O(\varepsilon ^{-1})\), which are large.

中文翻译：

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具有两个慢变量的3D等熵可压缩纳维-斯托克斯方程的全局解

在Lu和Zhang (J Differ Equ 376:406–468, 2023)的推动下，我们证明了具有在两个方向上缓慢变化的平滑初始数据的三维等熵可压缩纳维-斯托克斯方程解的全局存在性。在这样的设置中，初始数据的\(L^2\)范数的阶数为\(O(\varepsilon ^{-1})\)，它很大。