Global Solutions of 3D Isentropic Compressible Navier–Stokes Equations with Two Slow Variables

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 \(L^2\) $L^2$ -norms of the initial data are of order \(O(\varepsilon ^{-1})\) $O({\epsilon }^{-1})$ , which are large.