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Sharp global nonlinear stability for temperature dependent viscosity convection.

Straughan, B. (2002) 'Sharp global nonlinear stability for temperature dependent viscosity convection.', Proceedings of the Royal Society A : mathematical, physical and engineering sciences., 458 (2023). pp. 1773-1782.

Abstract

With regard to the dependence of viscosity on temperature, an unconditional non-linear energy-stability analysis for thermal convection according to Navier-Stokes theory has not yet been developed. We here analyse three models of fluid behaviour proposed by O. A. Ladyzhenskaya. We show that by using these theories we can develop an unconditional analysis directly. Two of the models lead directly to an unconditional development employing L2 theory, while the third necessitates the introduction of a generalized energy also involving an L3 term. The nonlinear stability boundaries in all three cases are sharp when compared with the instability thresholds of linear theory.

Item Type:Article
Keywords:Unconditional, Stability, Temperature-dependent viscosity, Thermal convection, Ladyzhenskaya's models,
Full text:Full text not available from this repository.
Publisher Web site:http://dx.doi.org/10.1098/rspa.2001.0945
Record Created:23 Apr 2007
Last Modified:09 Sep 2014 11:00

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