@Article{AAM-38-261,
author = {Zhang , PanLiu , Mengmeng and Song , Fangying},
title = {On Instability of the Rayleigh–Bénard Problem Without Thermal Diffusion in a Bounded Domain under $L^1$ -Norm},
journal = {Annals of Applied Mathematics},
year = {2022},
volume = {38},
number = {3},
pages = {261--279},
abstract = {<p style="text-align: justify;">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 $L^1$-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 $L^1$-norm.</p>},
issn = {},
doi = {https://doi.org/10.4208/aam.OA-2020-0060},
url = {http://global-sci.org/intro/article_detail/aam/20878.html}
}