发表机构
Nanjing Forestry University; Anhui University（南京林业大学; 安徽大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文在临界Besov空间中证明具有代数闭包的可压缩双流体模型在低马赫数极限下，对大且不良初值存在有限时间解并收敛到不可压缩Navier--Stokes流，通过高-中-低频分析和滤波技术获得新先验估计。
AI 中文摘要
本文研究了在$d$维环面（$d \geq 2$）上具有代数闭包的不可压缩双流体模型的低马赫数极限。对于临界Besov空间中的大且不良初值，我们证明了：只要马赫数足够小，重标度的可压缩双流体流在临界Besov空间中存在于不超过不可压缩流寿命的任何有限时间内。此外，当马赫数趋于零时，重标度的可压缩双流体流收敛到不可压缩Navier--Stokes流。证明基于对密度和速度场的高-中-低频分析，并结合涉及波算子的滤波技术。主要新颖之处在于推导了可压缩双流体模型解的高-中频部分的新先验估计，该估计显式依赖于时间、频率参数和马赫数。据我们所知，这是第一个在临界框架下证明可压缩双流体模型在低马赫数极限中对于大且不良初值具有（几乎）全局收敛性的工作。
英文摘要
In this paper, we study the low Mach number limit for a compressible two-fluid model with algebraic closure in the $d$-dimensional torus with $d \geq 2$. For large and ill-prepared initial data in critical Besov spaces, we prove that, provided that the Mach number is sufficiently small, the rescaled compressible two-fluid flow exists in critical Besov spaces for any finite time not exceeding the lifespan of the incompressible flow. Moreover, the rescaled compressible two-fluid flow converges to the incompressible Navier--Stokes flow as the Mach number tends to zero. The proof is based on a high-middle-low frequency analysis of the densities and velocity field, combined with a filtering technique involving wave operators. The main novelty is the derivation of new a priori estimates for the high-middle frequency part of the solution to the compressible two-fluid model, depending explicitly on time, the frequency parameter and the Mach number. To the best of our knowledge, this is the first work that proves (almost) global convergence for large and ill-prepared initial data in the low Mach number limit for compressible two-fluid model in critical framework.
