Abstract
Stability of stationary solutions of the Oberbeck–Boussinesq system (OB) and the corresponding artificial compressible system is considered. The latter system is obtained by adding the time derivative of the pressure with small parameter ε> 0 to the continuity equation of (OB), which was proposed by A. Chorin to find stationary solutions of (OB) numerically. Both systems have the same sets of stationary solutions and the system (OB) is obtained from the artificial compressible one as the limit ε→ 0 which is a singular limit. It is proved that if a stationary solution of the artificial compressible system is stable for sufficiently small ε> 0 , then it is also stable as a solution of (OB). The converse is proved provided that the velocity field of the stationary solution satisfies some smallness condition.
| Original language | English |
|---|---|
| Pages (from-to) | 345-365 |
| Number of pages | 21 |
| Journal | Journal of Mathematical Fluid Mechanics |
| Volume | 19 |
| Issue number | 2 |
| DOIs | |
| Publication status | Published - Jun 1 2017 |
Fingerprint
All Science Journal Classification (ASJC) codes
- Mathematical Physics
- Condensed Matter Physics
- Computational Mathematics
- Applied Mathematics
Cite this
On Chorin’s Method for Stationary Solutions of the Oberbeck–Boussinesq Equation. / Kagei, Yoshiyuki; Nishida, Takaaki.
In: Journal of Mathematical Fluid Mechanics, Vol. 19, No. 2, 01.06.2017, p. 345-365.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - On Chorin’s Method for Stationary Solutions of the Oberbeck–Boussinesq Equation
AU - Kagei, Yoshiyuki
AU - Nishida, Takaaki
PY - 2017/6/1
Y1 - 2017/6/1
N2 - Stability of stationary solutions of the Oberbeck–Boussinesq system (OB) and the corresponding artificial compressible system is considered. The latter system is obtained by adding the time derivative of the pressure with small parameter ε> 0 to the continuity equation of (OB), which was proposed by A. Chorin to find stationary solutions of (OB) numerically. Both systems have the same sets of stationary solutions and the system (OB) is obtained from the artificial compressible one as the limit ε→ 0 which is a singular limit. It is proved that if a stationary solution of the artificial compressible system is stable for sufficiently small ε> 0 , then it is also stable as a solution of (OB). The converse is proved provided that the velocity field of the stationary solution satisfies some smallness condition.
AB - Stability of stationary solutions of the Oberbeck–Boussinesq system (OB) and the corresponding artificial compressible system is considered. The latter system is obtained by adding the time derivative of the pressure with small parameter ε> 0 to the continuity equation of (OB), which was proposed by A. Chorin to find stationary solutions of (OB) numerically. Both systems have the same sets of stationary solutions and the system (OB) is obtained from the artificial compressible one as the limit ε→ 0 which is a singular limit. It is proved that if a stationary solution of the artificial compressible system is stable for sufficiently small ε> 0 , then it is also stable as a solution of (OB). The converse is proved provided that the velocity field of the stationary solution satisfies some smallness condition.
UR - http://www.scopus.com/inward/record.url?scp=85019268141&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85019268141&partnerID=8YFLogxK
U2 - 10.1007/s00021-016-0284-3
DO - 10.1007/s00021-016-0284-3
M3 - Article
AN - SCOPUS:85019268141
VL - 19
SP - 345
EP - 365
JO - Journal of Mathematical Fluid Mechanics
JF - Journal of Mathematical Fluid Mechanics
SN - 1422-6928
IS - 2
ER -