Hao Liu, Ruixin Zeng, Chengrong Zhang
Abstract:
This article studies the nonlinear stability of two-dimensional (2D) incompressible
magnetic Benard fluids near hydrostatic equilibrium in the absence of viscosity.
We prove the global well-posedness in Besov space by utilizing a frequency decomposition
approach, based on the potential hyperbolic structure. Furthermore, under appropriate
additional conditions on low-frequency part.
We derive a Lyapunov-type differential inequality and establish the optimal temporal
decay rates for the global solution, in the sense that the obtained decay rates coincide
with those of the associated linear heat semigroup and therefore cannot be improved in
general. Compared with the results in [30]
our findings not only provide the precise decay rates but also demonstrate faster
decay than those previously obtained.
Submitted August 25, 2025. Published February 20, 2026.
Math Subject Classifications: 35A01, 35B35, 35B40, 76W05.
Key Words: Magnetic Benard fluids; frequency decomposition; nonlinear stability; optimal temporal decay rates.
DOI: 10.58997/ejde.2026.17
Show me the PDF file (371 KB), TEX file for this article.
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Hao Liu School of Mathematics and Statistics Fuzhou University Fuzhou, 350108, China email: liuh20230111@163.com |
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Ruixin Zeng School of Mathematics and Statistics, Fuzhou University Fuzhou, 350108, China email: zengrx979@163.com |
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Chengrong Zhang School of Mathematics and Statistics Fuzhou University Fuzhou, 350108, China email: zhangcr3115@163.com |
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