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| Pattern Formations in Heat Convection Problems |
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Citation： |
Takaaki NISHIDA,Yoshiaki TERAMOTO.Pattern Formations in Heat Convection Problems[J].Chinese Annals of Mathematics B,2009,30(6):769~784 |
| Page view： 1804
Net amount： 1585 |
Authors： |
Takaaki NISHIDA; Yoshiaki TERAMOTO; |
Foundation： |
JSPS KAKENHI (No. 20540141). |
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| Abstract： |
After B′enard’s experiment in 1900, Rayleigh formulated heat convection prob-
lems by the Oberbeck-Boussinesq approximation in the horizontal strip domain in 1916.
The pattern formations have been investigated by the bifurcation theory, weakly nonlinear
theories and computational approaches. The boundary conditions for the velocity on the
upper and lower boundaries are usually assumed as stress-free or no-slip. In the first part
of this paper, some bifurcation pictures for the case of the stress-free on the upper bound-
ary and the no-slip on the lower boundary are obtained. In the second part of this paper,
the bifurcation pictures for the case of the stress-free on both boundaries by a computer
assisted proof are verified. At last, B′enard-Marangoni heat convections for the case of the
free surface of the upper boundary are considered. |
Keywords： |
Oberbeck-Boussinesq equation, Heat convection, Pattern formation,
Computer assisted proof |
Classification： |
65N15, 37M20, 35Q30 |
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