发表机构
Institute of Applied Physics and Computational Mathematics; School of Mathematics, Renmin University of China（应用物理与计算数学研究所; 中国人民大学数学学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文严格证明了三维有界域中全可压缩Navier-Stokes方程在无滑移边界条件和大温度变化下的低马赫数极限，通过构造能量泛函和Stokes提升获得一致估计。
AI 中文摘要
本文严格论证了在三维光滑有界区域中，满足速度无滑移边界条件和良好准备初始数据的全可压缩Navier-Stokes方程的低马赫数极限。在存在热传导和大温度变化的情况下，我们通过在Sobolev框架中构造能量泛函，建立了在独立于马赫数的时间区间上强解的一致估计。无滑移边界条件无法提供滑移边界情形中所使用的涡度边界关系。一个关键要素是采用修正速度时间导数的边界迹的无散度Stokes提升，来定义一个在边界上消失的测试函数。
英文摘要
In this paper, we rigorously justify the low Mach number limit of the full compressible Navier-Stokes equations in a three-dimensional smooth bounded domain, subject to the no-slip boundary condition for the velocity and well-prepared initial data. In the presence of heat conduction and large temperature variations, we establish the uniform estimates for strong solutions on a time interval independent of the Mach number by constructing an energy functional in a Sobolev framework. The no-slip boundary condition cannot provide the vorticity boundary relation used in the slip-boundary setting. A key ingredient is to employ a divergence-free Stokes lifting of the boundary trace of the time derivative of modified velocity to define a test function vanishing on the boundary.
Comments54 pages, no figures
