Nonlocal abstract Stokes equations and applications

Nonlocal abstract Stokes equations and applications | 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PDF Research Article Nonlocal abstract Stokes equations and applications Veli Shakhmurov This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-4029204/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 In this paper, the Cauchy problem for the stationary and instationary nonlocal imcompressible abstract Stokes equation is considered. The equation involve a convolution term and an abstract operator in a Banach space E on leading part. The existence, uniqueness and coercive estimates are derived in L p spaces. We, can obtain different classes of Stokes equations by choosing the space E and the linear operator A which occur in a wide variety of physical systems. In application the existence, uniqueness and L p -maximal regularity properties to solution of initial value problems for nonlocal degenerate Stokes equations and nonlocal Stokes equations with discontinuous coefficients are established AMS: 35Q30, 76D05, 34G10, 35J25 Stokes systems Elliptic and parabolic equations Semigroups of operators Boundary value problems Abstract differential equations Maximal Lp regularity 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-4029204","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":277179496,"identity":"78d053fe-898a-4576-80aa-79ad30f064d1","order_by":0,"name":"Veli Shakhmurov","email":"data:image/png;base64,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","orcid":"","institution":"Antalya Bilim University","correspondingAuthor":true,"submittingAuthor":false,"prefix":"","firstName":"Veli","middleName":"","lastName":"Shakhmurov","suffix":""}],"badges":[],"createdAt":"2024-03-07 17:07:39","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-4029204/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-4029204/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":52729392,"identity":"31dd8a7f-3f95-492f-8726-705641008ba2","added_by":"auto","created_at":"2024-03-15 04:31:02","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":275529,"visible":true,"origin":"","legend":"","description":"","filename":"VeliStoces7.pdf","url":"https://assets-eu.researchsquare.com/files/rs-4029204/v1_covered_c37c9d53-7e05-42cb-ae4f-38a8c26d44dd.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Nonlocal abstract Stokes equations and applications","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"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":"Stokes systems, Elliptic and parabolic equations, Semigroups of operators, Boundary value problems, Abstract differential equations, Maximal Lp regularity","lastPublishedDoi":"10.21203/rs.3.rs-4029204/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-4029204/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eIn this paper, the Cauchy problem for the stationary and instationary nonlocal imcompressible abstract Stokes equation is considered. The equation involve a convolution term and an abstract operator in a Banach space E on leading part. The existence, uniqueness and coercive estimates are derived in L\u003csup\u003ep\u003c/sup\u003e spaces. We, can obtain different classes of Stokes equations by choosing the space E and the linear operator A which occur in a wide variety of physical systems. 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