The Free Boundary of Steady Axisymmetric Inviscid Flow with Vorticity I: Near the Degenerate Point

In this paper, we investigate the singularity near the degenerate points of the steady axisymmetric flow with general vorticity of an inviscid incompressible fluid acted on by gravity and with a free surface. We called the points on the free boundary at which the gradient of the stream function vani...

Full description

Saved in:
Bibliographic Details
Published in:Communications in mathematical physics 2023-06, Vol.400 (3), p.2137-2179
Main Authors: Du, Lili, Huang, Jinli, Pu, Yang
Format: Article
Language:English
Subjects:
Axisymmetric flow
Classical and Quantum Gravitation
Complex Systems
Cusps
Flatness
Fluid flow
Free boundaries
Free surfaces
Incompressible flow
Incompressible fluids
Inviscid flow
Mathematical and Computational Physics
Mathematical Physics
Physics
Physics and Astronomy
Quantum Physics
Relativity Theory
Singularities
Stream functions (fluids)
Theoretical
Vorticity
Citations: Items that this one cites
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
cited_by
cites cdi_FETCH-LOGICAL-c270t-af4fe36bf00b181b35f2d0bbe415080edf31c9d693e44fb538a9c83a1ec95293
container_end_page 2179
container_issue 3
container_start_page 2137
container_title Communications in mathematical physics
container_volume 400
creator Du, Lili
Huang, Jinli
Pu, Yang
description In this paper, we investigate the singularity near the degenerate points of the steady axisymmetric flow with general vorticity of an inviscid incompressible fluid acted on by gravity and with a free surface. We called the points on the free boundary at which the gradient of the stream function vanishes as the degenerate points. The main results in this paper give the different classifications of the singularity near the degenerate points on the free surface. More precisely, we obtained that at the stagnation points, the possible profiles must be a Stokes corner, a horizontal cusp, or a horizontal flatness. At the degenerate points on the symmetric axis except the origin, the wave profile must be a cusp. At the origin, the possible wave profiles must be a Garabedian pointed bubble, a horizontal cusp, or a horizontal flatness.
doi_str_mv 10.1007/s00220-023-04651-7
format article
fullrecord <record><control><sourceid>proquest_cross</sourceid><recordid>TN_cdi_proquest_journals_2821007583</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>2821007583</sourcerecordid><originalsourceid>FETCH-LOGICAL-c270t-af4fe36bf00b181b35f2d0bbe415080edf31c9d693e44fb538a9c83a1ec95293</originalsourceid><addsrcrecordid>eNp9kE1LAzEURYMoWKt_wFXAdfQlmU93tVotFBUsbkNm5qVNaWdqklrn3zt1BHeu3ubce3mHkEsO1xwgvfEAQgADIRlEScxZekQGPJKCQc6TYzIA4MBkwpNTcub9CgBykSQDUsyXSCcOkd41u7rSrqWNoW8BddXS0Zf17WaDwdmSTutP60tb0cm62dO9DUv63rhgSxtaOr2lz6gdDV3bPS6wRqcD0tfG1uGcnBi99njxe4dkPnmYj5_Y7OVxOh7NWClSCEybyKBMCgNQ8IwXMjaigqLAiMeQAVZG8jKvklxiFJkilpnOy0xqjmUei1wOyVVfu3XNxw59UKtm5-puUYlMHCzFmewo0VOla7x3aNTW2U33tuKgDpDqVapOpfpRqdIuJPuQ7-B6ge6v-p_UNy_5dmo</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>2821007583</pqid></control><display><type>article</type><title>The Free Boundary of Steady Axisymmetric Inviscid Flow with Vorticity I: Near the Degenerate Point</title><source>Springer Nature</source><creator>Du, Lili ; Huang, Jinli ; Pu, Yang</creator><creatorcontrib>Du, Lili ; Huang, Jinli ; Pu, Yang</creatorcontrib><description>In this paper, we investigate the singularity near the degenerate points of the steady axisymmetric flow with general vorticity of an inviscid incompressible fluid acted on by gravity and with a free surface. We called the points on the free boundary at which the gradient of the stream function vanishes as the degenerate points. The main results in this paper give the different classifications of the singularity near the degenerate points on the free surface. More precisely, we obtained that at the stagnation points, the possible profiles must be a Stokes corner, a horizontal cusp, or a horizontal flatness. At the degenerate points on the symmetric axis except the origin, the wave profile must be a cusp. At the origin, the possible wave profiles must be a Garabedian pointed bubble, a horizontal cusp, or a horizontal flatness.</description><identifier>ISSN: 0010-3616</identifier><identifier>EISSN: 1432-0916</identifier><identifier>DOI: 10.1007/s00220-023-04651-7</identifier><language>eng</language><publisher>Berlin/Heidelberg: Springer Berlin Heidelberg</publisher><subject>Axisymmetric flow ; Classical and Quantum Gravitation ; Complex Systems ; Cusps ; Flatness ; Fluid flow ; Free boundaries ; Free surfaces ; Incompressible flow ; Incompressible fluids ; Inviscid flow ; Mathematical and Computational Physics ; Mathematical Physics ; Physics ; Physics and Astronomy ; Quantum Physics ; Relativity Theory ; Singularities ; Stream functions (fluids) ; Theoretical ; Vorticity</subject><ispartof>Communications in mathematical physics, 2023-06, Vol.400 (3), p.2137-2179</ispartof><rights>The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><cites>FETCH-LOGICAL-c270t-af4fe36bf00b181b35f2d0bbe415080edf31c9d693e44fb538a9c83a1ec95293</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>314,780,784,27924,27925</link.rule.ids></links><search><creatorcontrib>Du, Lili</creatorcontrib><creatorcontrib>Huang, Jinli</creatorcontrib><creatorcontrib>Pu, Yang</creatorcontrib><title>The Free Boundary of Steady Axisymmetric Inviscid Flow with Vorticity I: Near the Degenerate Point</title><title>Communications in mathematical physics</title><addtitle>Commun. Math. Phys</addtitle><description>In this paper, we investigate the singularity near the degenerate points of the steady axisymmetric flow with general vorticity of an inviscid incompressible fluid acted on by gravity and with a free surface. We called the points on the free boundary at which the gradient of the stream function vanishes as the degenerate points. The main results in this paper give the different classifications of the singularity near the degenerate points on the free surface. More precisely, we obtained that at the stagnation points, the possible profiles must be a Stokes corner, a horizontal cusp, or a horizontal flatness. At the degenerate points on the symmetric axis except the origin, the wave profile must be a cusp. At the origin, the possible wave profiles must be a Garabedian pointed bubble, a horizontal cusp, or a horizontal flatness.</description><subject>Axisymmetric flow</subject><subject>Classical and Quantum Gravitation</subject><subject>Complex Systems</subject><subject>Cusps</subject><subject>Flatness</subject><subject>Fluid flow</subject><subject>Free boundaries</subject><subject>Free surfaces</subject><subject>Incompressible flow</subject><subject>Incompressible fluids</subject><subject>Inviscid flow</subject><subject>Mathematical and Computational Physics</subject><subject>Mathematical Physics</subject><subject>Physics</subject><subject>Physics and Astronomy</subject><subject>Quantum Physics</subject><subject>Relativity Theory</subject><subject>Singularities</subject><subject>Stream functions (fluids)</subject><subject>Theoretical</subject><subject>Vorticity</subject><issn>0010-3616</issn><issn>1432-0916</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2023</creationdate><recordtype>article</recordtype><recordid>eNp9kE1LAzEURYMoWKt_wFXAdfQlmU93tVotFBUsbkNm5qVNaWdqklrn3zt1BHeu3ubce3mHkEsO1xwgvfEAQgADIRlEScxZekQGPJKCQc6TYzIA4MBkwpNTcub9CgBykSQDUsyXSCcOkd41u7rSrqWNoW8BddXS0Zf17WaDwdmSTutP60tb0cm62dO9DUv63rhgSxtaOr2lz6gdDV3bPS6wRqcD0tfG1uGcnBi99njxe4dkPnmYj5_Y7OVxOh7NWClSCEybyKBMCgNQ8IwXMjaigqLAiMeQAVZG8jKvklxiFJkilpnOy0xqjmUei1wOyVVfu3XNxw59UKtm5-puUYlMHCzFmewo0VOla7x3aNTW2U33tuKgDpDqVapOpfpRqdIuJPuQ7-B6ge6v-p_UNy_5dmo</recordid><startdate>20230601</startdate><enddate>20230601</enddate><creator>Du, Lili</creator><creator>Huang, Jinli</creator><creator>Pu, Yang</creator><general>Springer Berlin Heidelberg</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>20230601</creationdate><title>The Free Boundary of Steady Axisymmetric Inviscid Flow with Vorticity I: Near the Degenerate Point</title><author>Du, Lili ; Huang, Jinli ; Pu, Yang</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c270t-af4fe36bf00b181b35f2d0bbe415080edf31c9d693e44fb538a9c83a1ec95293</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2023</creationdate><topic>Axisymmetric flow</topic><topic>Classical and Quantum Gravitation</topic><topic>Complex Systems</topic><topic>Cusps</topic><topic>Flatness</topic><topic>Fluid flow</topic><topic>Free boundaries</topic><topic>Free surfaces</topic><topic>Incompressible flow</topic><topic>Incompressible fluids</topic><topic>Inviscid flow</topic><topic>Mathematical and Computational Physics</topic><topic>Mathematical Physics</topic><topic>Physics</topic><topic>Physics and Astronomy</topic><topic>Quantum Physics</topic><topic>Relativity Theory</topic><topic>Singularities</topic><topic>Stream functions (fluids)</topic><topic>Theoretical</topic><topic>Vorticity</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Du, Lili</creatorcontrib><creatorcontrib>Huang, Jinli</creatorcontrib><creatorcontrib>Pu, Yang</creatorcontrib><collection>CrossRef</collection><jtitle>Communications in mathematical physics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Du, Lili</au><au>Huang, Jinli</au><au>Pu, Yang</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>The Free Boundary of Steady Axisymmetric Inviscid Flow with Vorticity I: Near the Degenerate Point</atitle><jtitle>Communications in mathematical physics</jtitle><stitle>Commun. Math. Phys</stitle><date>2023-06-01</date><risdate>2023</risdate><volume>400</volume><issue>3</issue><spage>2137</spage><epage>2179</epage><pages>2137-2179</pages><issn>0010-3616</issn><eissn>1432-0916</eissn><abstract>In this paper, we investigate the singularity near the degenerate points of the steady axisymmetric flow with general vorticity of an inviscid incompressible fluid acted on by gravity and with a free surface. We called the points on the free boundary at which the gradient of the stream function vanishes as the degenerate points. The main results in this paper give the different classifications of the singularity near the degenerate points on the free surface. More precisely, we obtained that at the stagnation points, the possible profiles must be a Stokes corner, a horizontal cusp, or a horizontal flatness. At the degenerate points on the symmetric axis except the origin, the wave profile must be a cusp. At the origin, the possible wave profiles must be a Garabedian pointed bubble, a horizontal cusp, or a horizontal flatness.</abstract><cop>Berlin/Heidelberg</cop><pub>Springer Berlin Heidelberg</pub><doi>10.1007/s00220-023-04651-7</doi><tpages>43</tpages></addata></record>
fulltext fulltext
identifier ISSN: 0010-3616
ispartof Communications in mathematical physics, 2023-06, Vol.400 (3), p.2137-2179
issn 0010-3616
1432-0916
language eng
recordid cdi_proquest_journals_2821007583
source Springer Nature
subjects Axisymmetric flow
Classical and Quantum Gravitation
Complex Systems
Cusps
Flatness
Fluid flow
Free boundaries
Free surfaces
Incompressible flow
Incompressible fluids
Inviscid flow
Mathematical and Computational Physics
Mathematical Physics
Physics
Physics and Astronomy
Quantum Physics
Relativity Theory
Singularities
Stream functions (fluids)
Theoretical
Vorticity
title The Free Boundary of Steady Axisymmetric Inviscid Flow with Vorticity I: Near the Degenerate Point
url http://sfxeu10.hosted.exlibrisgroup.com/loughborough?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2024-12-27T01%3A37%3A19IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest_cross&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=The%20Free%20Boundary%20of%20Steady%20Axisymmetric%20Inviscid%20Flow%20with%20Vorticity%20I:%20Near%20the%20Degenerate%20Point&rft.jtitle=Communications%20in%20mathematical%20physics&rft.au=Du,%20Lili&rft.date=2023-06-01&rft.volume=400&rft.issue=3&rft.spage=2137&rft.epage=2179&rft.pages=2137-2179&rft.issn=0010-3616&rft.eissn=1432-0916&rft_id=info:doi/10.1007/s00220-023-04651-7&rft_dat=%3Cproquest_cross%3E2821007583%3C/proquest_cross%3E%3Cgrp_id%3Ecdi_FETCH-LOGICAL-c270t-af4fe36bf00b181b35f2d0bbe415080edf31c9d693e44fb538a9c83a1ec95293%3C/grp_id%3E%3Coa%3E%3C/oa%3E%3Curl%3E%3C/url%3E&rft_id=info:oai/&rft_pqid=2821007583&rft_id=info:pmid/&rfr_iscdi=true