A boundary value problem of thermal convection

Document Type

Article

Publication Date

1-1-1980

Abstract

The two-dimensional thermal convection of a viscous fluid in a rectangular region is analyzed using the Boussinesq theory, and the Rayleigh boundary conditions. The existence of a unique convention state bifurcating from each eigenvalue of the linearized theory is established by using the Morse lemma. This establishes the validity of the formal perturbation method for determining the convection states. The effects of imperfections on the transition from the conduction to the convection states are studied. A theorem of Thom is used to justify a previous asymptotic expansion method near the critical Rayleigh number. © 1980.

Identifier

49149142162 (Scopus)

Publication Title

Journal of Differential Equations

External Full Text Location

https://doi.org/10.1016/0022-0396(80)90048-0

e-ISSN

10902732

ISSN

00220396

First Page

45

Last Page

54

Issue

1

Volume

35

Grant

X00014-76-6-0010

Fund Ref

National Science Foundation

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