The present paper is dedicated to the study of the Cauchy problem for compressible Navier–Stokes–Poisson–Korteweg model in any dimension $d \geq 2$, which simultaneously involves the lower order potential term and the higher order capillarity term. The unique global solvability of the system is obtained when the initial data are close to a stable equilibrium state in a functional setting invariant by the scaling of the associated equations. In particular, one may construct the unique global solution for a class of large highly oscillating initial velocities in physical dimensions $d=2,3$.

中文翻译：

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多维可压缩Navier–Stokes–Poisson–Korteweg模型的独特全局可解性

本文致力于研究任意维数$ d \ geq 2 $的可压缩Navier–Stokes–Poisson–Korteweg模型的柯西问题，该问题同时涉及低阶势项和高阶毛细管项。当初始数据在函数设置中通过相关方程的缩放不变而接近稳定的平衡状态时，可获得系统的唯一全局可解性。特别地，对于一类物理尺寸为$ d = 2,3 $的大的高振荡初始速度，可以构造唯一的全局解决方案。