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Unstable spectrum of a Rayleigh–Bénard system with variable viscosity
Olivier Lafitte1, 2 
1 IRL CRM, UMI3457, Centre de recherches Mathématiques, Université de Montréal, Montréal, Canada.
2 LAGA, UMR7539, Université Sorbonne Paris Nord, 93430 Villetaneuse, France.
Comptes Rendus. Mathématique, Volume 359 (2021) no. 9, pp. 1165-1178.

This Note studies a Rayleigh–Bénard system in an infinite layer, in the case of temperature-dependent viscosity, with rigid boundary conditions for the velocity at the bottom and free-slip at a top of the layer. It states the linearized problem in the relevant functional operator set-up and identifies, for each nonzero transverse frequency k and Rayleigh number R the (finite) number of modes which are unstable in time. This number is equal to the number of eigenvalues of a particular operator which are smaller than R.

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Accepté le :
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DOI : 10.5802/crmath.232
Classification : 34L05, 76E15

Olivier Lafitte 1, 2

1 IRL CRM, UMI3457, Centre de recherches Mathématiques, Université de Montréal, Montréal, Canada.
2 LAGA, UMR7539, Université Sorbonne Paris Nord, 93430 Villetaneuse, France.
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
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     title = {Unstable spectrum of a {Rayleigh{\textendash}B\'enard} system with variable viscosity},
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     pages = {1165--1178},
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Olivier Lafitte. Unstable spectrum of a Rayleigh–Bénard system with variable viscosity. Comptes Rendus. Mathématique, Volume 359 (2021) no. 9, pp. 1165-1178. doi : 10.5802/crmath.232. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.232/

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