AI 中文总结
该研究证明了可压缩纳维-斯托克斯-科特韦格方程组的抛物型松弛形式的初边值问题存在有限能量弱解的全局时间存在性，其基于三级近似格式等方法，将可压缩纳维-斯托克斯方程的对应结果推广到松弛系统。
AI 中文摘要
我们研究可压缩纳维-斯托克斯-科特韦格方程组的抛物型松弛形式，证明其对应的初边值问题存在有限能量弱解的全局时间存在性。我们的证明基于三级近似格式、有效粘性通量的弱紧性性质以及抛物型正则性估计。该结果适用于多种非单调压力函数，将已知的可压缩纳维-斯托克斯方程的对应结果推广到了松弛方程组。
英文摘要
We consider a parabolic relaxation formulation of the compressible Navier-Stokes-Korteweg system and prove the global-in-time existence of finite energy weak solutions to the associated initial-boundary-value-problem. Our proof is based on a three-level approximation scheme, a weak compactness property of the effective viscous flux, and parabolic regularity estimates. Our result holds for a broad variety of non-monotone pressure functions and generalizes the corresponding results known for the compressible Navier-Stokes equations to the relaxation system.
