On Instability of the Rayleigh–Bénard Problem Without Thermal Diffusion in a Bounded Domain under L1 -Norm
Year: 2022
Author: Pan Zhang, Mengmeng Liu, Fangying Song
Annals of Applied Mathematics, Vol. 38 (2022), Iss. 3 : pp. 261–279
Abstract
We investigate the thermal instability of a three-dimensional Rayleigh–Bénard (RB for short) problem without thermal diffusion in a bounded domain. First we construct unstable solutions in exponential growth modes for the linear RB problem. Then we derive energy estimates for the nonlinear solutions by a method of a prior energy estimates, and establish a Gronwall-type energy inequality for the nonlinear solutions. Finally, we estimate for the error of L1-norm between the both solutions of the linear and nonlinear problems, and prove the existence of escape times of nonlinear solutions. Thus we get the instability of nonlinear solutions under L1-norm.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/aam.OA-2020-0060
Annals of Applied Mathematics, Vol. 38 (2022), Iss. 3 : pp. 261–279
Published online: 2022-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 19
Keywords: Rayleigh–Bénard problem thermal instability initial-boundary value problem.