This paper is concerned with an initial and boundary value problem of the Navier‐Stokes equations for compressible viscous barotropic flow subject to large external potential forces in a half space ${ℝ}_{+}^3$ with Navier's boundary conditions. The global well‐posedness of strong solutions with large oscillations and vacuum is established, provided that the initial energy is suitably small and that the unique steady state is strictly away from vacuum. As a by‐product, the stability of stationary solution is obtained.

中文翻译：

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在可压缩粘性正压流中，在Navier边界条件下，它在半空间中受到较大的外势力的作用

本文涉及可压缩粘性正压流在半空间中承受较大外势的情况下Navier-Stokes方程的初值和边值问题 ${ℝ}_{+}^3$Navier的边界条件。只要初始能量适当地小并且唯一的稳态严格远离真空，就可以建立具有大振动和真空的强解的整体适定性。作为副产品，可以获得固定溶液的稳定性。