Global Classical Solutions to the viscous two-phase flow model with slip Boundary Conditions in 3D Exterior Domains

Global Classical Solutions to the viscous two-phase flow model with slip Boundary Conditions in 3D Exterior Domains | 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 Global Classical Solutions to the viscous two-phase flow model with slip Boundary Conditions in 3D Exterior Domains Zilai Li, Hao Liu, Huaqiao Wang, Daoguo Zhou This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-2610278/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 24 Apr, 2023 Read the published version in Boundary Value Problems → Version 1 posted 7 You are reading this latest preprint version Abstract We consider the two-phase flow model in 3D exterior domains with slip boundary conditions. We establish the global existence of classical solutions of this system provided that the initial energy is suitably small. Furthermore, we prove that the pressure has large oscillations and contains vacuum states when the initial pressure allows large oscillations and a vacuum. Finally, we also obtain the large-time behavior of the classical solutions. 2010 Mathematics Subject Classification. 35Q35; 35Q30; 35A09; 35B40. two-phase flow model global existence slip boundary condition exterior domains vacuum large-time behavior Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Published Journal Publication published 24 Apr, 2023 Read the published version in Boundary Value Problems → Version 1 posted Editorial decision: Major revision 06 Mar, 2023 Reviews received at journal 03 Mar, 2023 Reviewers agreed at journal 23 Feb, 2023 Reviewers invited by journal 23 Feb, 2023 Editor assigned by journal 23 Feb, 2023 Submission checks completed at journal 22 Feb, 2023 First submitted to journal 20 Feb, 2023 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. 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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-2610278","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":178217983,"identity":"2db9c6f8-03b8-48e8-9761-814ecf4ead0b","order_by":0,"name":"Zilai Li","email":"","orcid":"","institution":"Henan Polytechnic University","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"Zilai","middleName":"","lastName":"Li","suffix":""},{"id":178217984,"identity":"a884cd8d-bf5e-45f5-8df4-250dc20999a7","order_by":1,"name":"Hao Liu","email":"","orcid":"","institution":"Henan Polytechnic University","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"Hao","middleName":"","lastName":"Liu","suffix":""},{"id":178217985,"identity":"f7d34509-aac8-4466-bf43-5322cde24c52","order_by":2,"name":"Huaqiao Wang","email":"","orcid":"","institution":"Chongqing University","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"Huaqiao","middleName":"","lastName":"Wang","suffix":""},{"id":178217986,"identity":"aa5f144f-cee7-4341-a732-2498fa3293be","order_by":3,"name":"Daoguo Zhou","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAwElEQVRIiWNgGAWjYDCCAxAqgYGB+QDJWtgSSNbCY0CcDr7jhw+/5qmoy+OXyPl44w2DnZxuAwEtkmfS0qx5zrAVS87I3Ww5hyHZ2OwAAS0GB3LMjHnbeBI33MjdJs3DcCBxG0Et59+AtEgAteQ8I1LLjRzjx7xtBiAtbMRpkbzxLI1xzpmExJk9z4wt5xgQ4Re+88mHP7ypqEvsZ09+eONNhZ0cQS1AwCYBY0kQGzXMHxBaiNMxCkbBKBgFIwwAALXhRCVGb760AAAAAElFTkSuQmCC","orcid":"","institution":"Henan Polytechnic University","correspondingAuthor":true,"submittingAuthor":false,"prefix":"","firstName":"Daoguo","middleName":"","lastName":"Zhou","suffix":""}],"badges":[],"createdAt":"2023-02-21 04:59:11","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-2610278/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-2610278/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1186/s13661-023-01733-2","type":"published","date":"2023-04-24T20:36:41+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":44726943,"identity":"7711fc6a-11a6-4152-a7c4-049e523569d3","added_by":"auto","created_at":"2023-10-16 20:50:27","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":484432,"visible":true,"origin":"","legend":"","description":"","filename":"zhou230221.pdf","url":"https://assets-eu.researchsquare.com/files/rs-2610278/v1_covered_596de036-40b1-452d-bef7-ba922238e9ee.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Global Classical Solutions to the viscous two-phase flow model with slip Boundary Conditions in 3D Exterior Domains","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"boundary-value-problems","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"bovp","sideBox":"Learn more about [Boundary Value Problems](http://boundaryvalueproblems.springeropen.com)","snPcode":"13661","submissionUrl":"https://submission.nature.com/new-submission/13661/3","title":"Boundary Value Problems","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":true},"keywords":"two-phase flow model, global existence, slip boundary condition, exterior domains, vacuum, large-time behavior","lastPublishedDoi":"10.21203/rs.3.rs-2610278/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-2610278/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eWe consider the \u0026nbsp;two-phase flow model in 3D exterior domains with slip boundary conditions. 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