Stability of the 2D Boussinesq-MHD System with Fractional Horizontal Dissipation

Stability of the 2D Boussinesq-MHD System with Fractional Horizontal Dissipation | Authorea try { document.documentElement.classList.add('js'); } catch (e) { } var _gaq = _gaq || []; _gaq.push(['_setAccount', 'G-8VDV14Y67G']); _gaq.push(['_trackPageview']); (function() { var ga = document.createElement('script'); ga.type = 'text/javascript'; ga.async = true; ga.src = ('https:' == document.location.protocol ? 'https://ssl' : 'http://www') + '.google-analytics.com/ga.js'; var s = document.getElementsByTagName('script')[0]; s.parentNode.insertBefore(ga, s); })(); Skip to main content Preprints Collections Wiley Open Research IET Open Research Ecological Society of Japan All Collections About About Authorea FAQs Contact Us Quick Search anywhere Search for preprint articles, keywords, etc. Search Search ADVANCED SEARCH SCROLL Mathematical Methods in the Applied Sciences This is a preprint and has not been peer reviewed. Data may be preliminary. 30 July 2025 V1 Latest version Share on Stability of the 2D Boussinesq-MHD System with Fractional Horizontal Dissipation Authors : YUAN SUN , YAOYAO GU 0009-0008-6214-9499 , and Qunyi Bie 0000-0002-9105-2652 Authors Info & Affiliations https://doi.org/10.22541/au.175387154.42513342/v1 Published Mathematical Methods in the Applied Sciences Version of record Peer review timeline 296 views 169 downloads Contents Abstract Supplementary Material Information & Authors Metrics & Citations View Options References Figures Tables Media Share Abstract This paper investigates the stability of perturbations near equilibrium states for the two-dimensional Boussinesq-magnetohydrodynamics(MHD) system with fractional horizontal dissipation in the domain Ω=T×R, where T=[0 , 1] is the one-dimensional periodic box. The absence of vertical dissipation, combined with the presence of fractional operators, presents significant challenges to the study of stability and long-time dynamics in the Boussinesq-MHD system. To address these issues, we leverage the orthogonal decomposition method in conjunction with multiple fractional anisotropic interpolation inequalities and a fractional Poincaré-type inequality within our analytical framework. We prove the global stability of the system when the initial data are sufficiently small in H 2 ( Ω ) . Moreover, as time tends to infinity, the oscillatory part of the solution converges exponentially to zero in H 1 ( Ω ) . Supplementary Material File (stability of the 2d boussinesq mhd system with fractional horizontal dissipation.pdf) Download 299.18 KB Information & Authors Information Version history V1 Version 1 30 July 2025 Peer review timeline Published Mathematical Methods in the Applied Sciences Version of Record 8 Jan 2026 Published Copyright This work is licensed under a Non Exclusive No Reuse License. Collection Mathematical Methods in the Applied Sciences Keywords boussinesq-mhd exponential decay fractional horizontal dissipation stability Authors Affiliations YUAN SUN Shanghai University of Electric Power View all articles by this author YAOYAO GU 0009-0008-6214-9499 Shanghai University of Electric Power View all articles by this author Qunyi Bie 0000-0002-9105-2652 China Three Gorges University View all articles by this author Metrics & Citations Metrics Article Usage 296 views 169 downloads .FvxKWukQNSOunydq8rnd { width: 100px; } Citations Download citation YUAN SUN, YAOYAO GU, Qunyi Bie. Stability of the 2D Boussinesq-MHD System with Fractional Horizontal Dissipation. Authorea . 30 July 2025. DOI: https://doi.org/10.22541/au.175387154.42513342/v1 If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download. For more information or tips please see 'Downloading to a citation manager' in the Help menu . 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