TY - JOUR
T1 - On the spectrum for the artificial compressible system
AU - Kagei, Yoshiyuki
AU - Nishida, Takaaki
AU - Teramoto, Yuka
N1 - Funding Information:
Y. Kagei was partly supported by JSPS KAKENHI Grant Number JP24340028 , JP15K13449 , JP24224003 , JP16H03947 ; T. Nishida was partly supported by JSPS KAKENHI Grant Number JP26400163 , JP17K05317 ; Y. Teramoto was partly supported by JSPS KAKENHI Grant Number JP17J04702 .
Publisher Copyright:
© 2017 Elsevier Inc.
PY - 2018/1/15
Y1 - 2018/1/15
N2 - 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 number ϵ which 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 small ϵ. The result is applied to the Taylor problem.
AB - 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 number ϵ which 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 small ϵ. The result is applied to the Taylor problem.
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U2 - 10.1016/j.jde.2017.09.026
DO - 10.1016/j.jde.2017.09.026
M3 - Article
AN - SCOPUS:85030784111
SN - 0022-0396
VL - 264
SP - 897
EP - 928
JO - Journal of Differential Equations
JF - Journal of Differential Equations
IS - 2
ER -