Mechanics
Unstable spectrum of a Rayleigh–Bénard system with variable viscosity
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 $R$.

Accepted:
Revised after acceptance:
Published online:
DOI: https://doi.org/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.
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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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