Existence and Uniqueness of Asymptotically Almost Periodic Mild Solutions for Magneto-micropolarFluid Equations on Real Hyperbolic Manifolds

Existence and Uniqueness of Asymptotically Almost Periodic Mild Solutions for Magneto-micropolarFluid Equations on Real Hyperbolic Manifolds | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Existence and Uniqueness of Asymptotically Almost Periodic Mild Solutions for Magneto-micropolarFluid Equations on Real Hyperbolic Manifolds Bobing Meng, Xiaochun Sun, Yuguo Liu, Jihong Zhang This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-9669813/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract This paper investigates the existence, uniqueness, and exponential stability of asymptotically almost periodic mild solutions to the magneto-micropolarfluid equations on three-dimensional real hyperbolic manifolds, after reformulatingthe original system as a pressure-free abstract evolution equation through the Ebin-Marsden viscous operator and the Kodaira-Hodge projection. Within this geometricframework, we establish the existence and uniqueness of asymptotically almost periodic mild solutions for the linear problem, together with the existence, uniqueness,and exponential stability of small solutions to the nonlinear system, by combiningsemigroup estimates on real hyperbolic manifolds with a Massera-type principle, afixed-point argument, and cone inequalities. Finally, numerical simulations are presented to illustrate the decay of perturbations, the bounded recurrent behaviorinduced by asymptotically almost periodic external forces, and the enhanced stabilizing effect produced by hyperbolic dissipation. Magneto-micropolar fluid equations Real hyperbolic manifolds Asymptotically almost periodic mild solutions Exponential stability Numerical simulations Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-9669813","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":640869726,"identity":"9f664303-690a-456b-878c-e50fa741053a","order_by":0,"name":"Bobing Meng","email":"","orcid":"","institution":"Northwest Normal University","correspondingAuthor":false,"prefix":"","firstName":"Bobing","middleName":"","lastName":"Meng","suffix":""},{"id":640869727,"identity":"7fbedcc1-3cac-4049-91e7-dff728a57e9f","order_by":1,"name":"Xiaochun Sun","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA40lEQVRIiWNgGAWjYLCCBCA2YGBgfADlGxCthRmmlAgtUGVsEkRpkZ+Re0ziQY2NvLlE7rHqwrY7iQ3szdskGGru4Db8Rl6yQcKxNMOdM/LSbs9se5bYwHOsTILh2DPcWiRyDB8ksB1OMLiRY3abd9vhxAaJHDMJxobDeByWY3Ag4R9ESzFYi/wb/FoYbgBtSWyDaGGG2MKDX4vBmTfGBol9aYYbgAxp3n+Hjdt40ootEo7hcVh7jpnkj2828gbHcww/85w5LNvPfnjjjQ81eByGAdhARAIJGkbBKBgFo2AUYAIAccVUh0LpQusAAAAASUVORK5CYII=","orcid":"","institution":"Northwest Normal University","correspondingAuthor":true,"prefix":"","firstName":"Xiaochun","middleName":"","lastName":"Sun","suffix":""},{"id":640869728,"identity":"47cd7c59-1693-492d-8ed9-fe9a3dc907f4","order_by":2,"name":"Yuguo Liu","email":"","orcid":"","institution":"Northwest Normal University","correspondingAuthor":false,"prefix":"","firstName":"Yuguo","middleName":"","lastName":"Liu","suffix":""},{"id":640869729,"identity":"4f5c4094-5dda-44c3-a5e9-25c5c8c900c4","order_by":3,"name":"Jihong Zhang","email":"","orcid":"","institution":"Lanzhou City University","correspondingAuthor":false,"prefix":"","firstName":"Jihong","middleName":"","lastName":"Zhang","suffix":""}],"badges":[],"createdAt":"2026-05-10 11:39:00","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-9669813/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-9669813/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":109799470,"identity":"17cc1011-4887-4e41-baf7-7466e69f9ab5","added_by":"auto","created_at":"2026-05-22 15:29:20","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1521661,"visible":true,"origin":"","legend":"","description":"","filename":"file.pdf","url":"https://assets-eu.researchsquare.com/files/rs-9669813/v1_covered_9b0a12bf-a5e2-4576-9790-87fc570b2c19.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Existence and Uniqueness of Asymptotically Almost Periodic Mild Solutions for Magneto-micropolarFluid Equations on Real Hyperbolic Manifolds","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"Magneto-micropolar fluid equations, Real hyperbolic manifolds, Asymptotically almost periodic mild solutions, Exponential stability, Numerical simulations","lastPublishedDoi":"10.21203/rs.3.rs-9669813/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-9669813/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"This paper investigates the existence, uniqueness, and exponential stability of asymptotically almost periodic mild solutions to the magneto-micropolarfluid equations on three-dimensional real hyperbolic manifolds, after reformulatingthe original system as a pressure-free abstract evolution equation through the Ebin-Marsden viscous operator and the Kodaira-Hodge projection. 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