三维Navier-Stokes-Fourier方程平面扩散波附近的低马赫数极限

中文摘要 AI 辅助

我们研究了在$\mathbb{R}\times\mathbb{T}^2$上三维完全可压缩Navier-Stokes-Fourier（NSF）方程的低马赫数极限，针对两类不同的初始数据，分别对应于良备（well-prepared）和不良备（ill-prepared）情形。密度和温度被允许在无穷远处趋近不同的渐近状态。对于良备情形，当马赫数趋于零时，可压缩NSF方程的解在时间上全局收敛到平面扩散波解，其中远场状态之间的差异与马赫数无关。此外，可以获得最优的时间衰减率。这可以被视为三维NSF方程在具有大温度变化情况下低马赫数极限的首个全局时间结果。对于不良备情形，通过对零模态和非零模态进行分离能量估计，并利用Métivier-Schochet在文献\cite{Métivier2001}中提出的辅助收敛引理，获得了相应的局部时间结果。需要指出的是，远场状态之间的差异允许任意大。

英文摘要

We investigate the low Mach number limit of the three-dimensional full compressible Navier-Stokes-Fourier (NSF) equations on \(\mathbb{R}\times\mathbb{T}^2\) for two different classes of initial data, corresponding respectively to a well-prepared regime and an ill-prepared regime. The density and temperature are allowed to approach different asymptotic states at infinity. For the well-prepared regime, the solutions of compressible NSF equations converge to a planar diffusion wave solution globally in time as the Mach number tends to zero, where the difference between the states at the far fields is small independently of the Mach number and the non-zero modes of the initial perturbations are exponentially small. Moreover, the optimal time-decay rate can be obtained. It can be viewed as the first global-in-time result on the low Mach number limit of three-dimensional NSF equations with large temperature variations. The corresponding local-in-time result is proved while the difference between the states at the far fields can be arbitrarily large for the ill-prepared data.

发表机构

• Institute of Applied Physics and Computational Mathematics（应用物理与计算数学研究所）
• National Key Laboratory of Computational Physics（计算物理学国家重点实验室）
• Department of Mathematics, The Chinese University of Hong Kong（香港中文大学数学系）
• Graduate School of China Academy of Engineering Physics（中国工程物理研究院研究生院）

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