On the spectrum for the artificial compressible system
On the spectrum for the artificial compressible system
复制标题
关于人工可压缩系统的频谱
DOI：
10.1016/j.jde.2017.09.026
复制
发表时间：
2018
影响因子：
2.4
通讯作者：
Yuka Teramoto
中科院分区：
文献类型：
--
作者：
Yoshiyuki Kagei;Takaaki Nishida;Yuka Teramoto
研究了不可压缩Navier-Stokes方程组和相应的人工可压缩方程组定常解的稳定性。这两个系统具有相同的定常解集，不可压缩系统是由人工可压缩系统在人工马赫数为零的奇异极限下得到的。利用变分方法证明了：如果不可压缩系统的定常解是渐近稳定的，且定常解的速度场满足能量型稳定性准则，且容许函数仅为速度场的势流部分，则对于足够小的扰动，定常解作为人工可压缩系统的解也是稳定的.将所得结果应用于泰勒问题。
Stability of stationary solutions of the incompressible Navier–Stokes system and the corresponding artificial compressible system is considered. Both systems have the same sets of stationary solutions and the incompressible system is obtained from the artificial compressible one in the zero limit of the artificial Mach numberϵwhich is a singular limit. It is proved that if a stationary solution of the incompressible system is asymptotically stable and the velocity field of the stationary solution satisfies an energy-type stability criterion by variational method with admissible functions being only potential flow parts of velocity fields, then it is also stable as a solution of the artificial compressible one for sufficiently smallϵ. The result is applied to the Taylor problem.