Analysis reveals global stability and exponential decay rate in a two-dimensional magnetic Bénard system, indicating effective thermal management strategies.
In this paper, we focus on the incompressible two‐dimensional magnetic Bénard system with fractional magnetic diffusion and thermal diffusivity in the horizontal direction in the domain . Global stability in and explicit exponential large‐time decay rate of the solution are obtained. Our analysis proceeds by decomposing quantities into a horizontal average and an oscillation component. A pivotal aspect of our analysis is to maximize the hidden dissipation within the equations.
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Yuanyuan Zhang (2025) studied this question.
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