GLOBAL FUJITA-KATO SOLUTIONS OF THE INCOMPRESSIBLE INHOMOGENEOUS MAGNETOHYDRODYNAMIC EQUATIONS

GLOBAL FUJITA-KATO SOLUTIONS OF THE INCOMPRESSIBLE INHOMOGENEOUS MAGNETOHYDRODYNAMIC EQUATIONS | 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 Search Search ADVANCED SEARCH SCROLL This is a preprint and has not been peer reviewed. Data may be preliminary. 30 January 2026 V1 Latest version Share on GLOBAL FUJITA-KATO SOLUTIONS OF THE INCOMPRESSIBLE INHOMOGENEOUS MAGNETOHYDRODYNAMIC EQUATIONS Authors : Fucai Li 0000-0003-1414-8818 , Jinkai Ni 0009-0009-4935-468X [email protected] , and Lingyun Shou 0000-0002-8299-5966 Authors Info & Affiliations https://doi.org/10.22541/au.176977277.77901684/v1 138 views 76 downloads Contents Abstract Supplementary Material Information & Authors Metrics & Citations View Options References Figures Tables Media Share Abstract We investigate the incompressible inhomogeneous magnetohydrodynamic equations in R 3, under the assumptions that the initial density ρ 0 is only bounded, and the initial velocity u 0 and magnetic field B 0 exhibit critical regularities. In particular, the density is allowed to be piecewise constant with jumps. First, we establish the global-in-time well-posedness and large-time behavior of solutions to the Cauchy problem in the case that ρ 0 has small variations, and u 0 and B 0 are sufficiently small in the critical Besov space B _ p, 1 3 /p − 1 with 1 3. Moreover, the small variation assumption on ρ 0 is no longer required in the case p=2. Then, we construct a unique global Fujita-Kato solution under the weaker condition that u 0 and B 0 are small in B _ 2, ∞ 1 / 2 but may be large in H _ 1 / 2 . Additionally, we show a general uniqueness result with only bounded and nonnegative density, without assuming the L 1 ( 0, T ; L ∞ ) regularity of the velocity. Supplementary Material File (lns-mhd-v17.pdf) Download 560.27 KB Information & Authors Information Version history V1 Version 1 30 January 2026 Copyright This work is licensed under a Non Exclusive No Reuse License. Keywords critical regularity discontinuous density fujita-kato solution incompressible inhomogeneous mhd equations uniqueness Authors Affiliations Fucai Li 0000-0003-1414-8818 Nanjing University View all articles by this author Jinkai Ni 0009-0009-4935-468X [email protected] Nanjing University View all articles by this author Lingyun Shou 0000-0002-8299-5966 Nanjing Normal University View all articles by this author Metrics & Citations Metrics Article Usage 138 views 76 downloads .FvxKWukQNSOunydq8rnd { width: 100px; } Citations Download citation Fucai Li, Jinkai Ni, Lingyun Shou. GLOBAL FUJITA-KATO SOLUTIONS OF THE INCOMPRESSIBLE INHOMOGENEOUS MAGNETOHYDRODYNAMIC EQUATIONS. Authorea . 30 January 2026. DOI: https://doi.org/10.22541/au.176977277.77901684/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. 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