带Dirichlet边界条件的三维非等熵Navier-Stokes方程强解的低马赫数极限（英文）  

Low Mach Number Limit of Strong Solutions to 3-D Full Navier-Stokes Equations with Dirichlet Boundary Condition

作　　者：郭柏灵[1] 曾兰 倪国喜[1] GUO Boling;ZENG Lan;NI Guoxi(Institute of Applied Physics and Computational Mathematics,Beijing,100088,P.R.China;Graduate School of China Academy of Engineering Physics,Beijing,100088,P.R.China)

机构地区：[1]北京应用物理与计算数学研究所,北京100088 [2]北京工程物理研究院研究生院,北京100088

出　　处：《数学进展》2019年第6期667-691,共25页Advances in Mathematics（China）

基　　金：Guo is Supported by NSFC(No.11731014)

摘　　要：本文研究了非等熵可压缩Navier-Stokes方程在三维有界区域中的低马赫数极限,其中速度满足Dirichlet边界条件,温度满足Neumann边界条件.假设当马赫数趋于零时初始密度和温度都接近常数,我们证明了强解在有限时间区间内关于马赫数的一致先验估计.进一步,我们证明了当马赫数趋于零时,非等熵可压缩Navier-Stokes方程的强解收敛到等熵不可压缩Navier-Stokes方程的解.In this paper,we consider the low Mach number limit of the full compressible Navier-Stokes equations in a three-dimensional bounded domain where the velocity field and the temperature satisfy the Dirichlet boundary conditions and the Neumann boundary condition,respectively.The uniform estimates in the Mach number for the strong solutions are derived in a short time interval,provided that the initial density and temperature are close to the constant states.Thus the solutions of the full compressible Navier-Stokes equations converge to the the isentropic incompressible Navier-Stokes equations,as the Mach number tends to zero.

关 键 词：不可压极限 非等熵Navier-Stokes方程 DIRICHLET边界条件 

分 类 号：O175.2[理学—数学]