Comptes Rendus
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.

Revised after acceptance:
Published online:
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.
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights
     author = {Olivier Lafitte},
     title = {Unstable spectrum of a {Rayleigh{\textendash}B\'enard} system with variable viscosity},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {1165--1178},
     publisher = {Acad\'emie des sciences, Paris},
     volume = {359},
     number = {9},
     year = {2021},
     doi = {10.5802/crmath.232},
     language = {en},
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PB  - Académie des sciences, Paris
DO  - 10.5802/crmath.232
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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.

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