The Zero-Mach Limit of Compressible Flows
The Zero-Mach Limit of Compressible Flows
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DOI：
10.1007/s002200050308
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发表时间：
1998-04
影响因子：
2.4
通讯作者：
D. Hoff
中科院分区：
文献类型：
--
作者：
D. Hoff
证明了二维和三维空间的可压缩纳维-斯托克斯流在马赫数趋于零的极限收敛为不可压缩纳维-斯托克斯流。对外力、初速度或时间间隔没有小的限制。我们假设不可压缩流存在并且在给定的时间区间上是相当平滑的，并证明具有相容初始数据的可压缩流在该时间区间上是一致收敛的。分析表明，这一过程的基本机制是非双曲效应，随着马赫数的减小，非双曲效应越来越强，并最终使密度趋于恒定。
We prove that compressible Navier-Stokes flows in two and three space dimensions converge to incompressible Navier-Stokes flows in the limit as the Mach number tends to zero. No smallness restrictions are imposed on the external force, the initial velocity, or the time interval. We assume instead that the incompressible flow exists and is reasonably smooth on a given time interval, and prove that compressible flows with compatible initial data converge uniformly on that time interval. Our analysis shows that the essential mechanism in this process is ahyperboliceffect which becomes stronger with smaller Mach number and which ultimately drives the density to a constant.