Local-in-time existence of a free-surface 3D Euler flow with H 2+δ initial vorticity in a neighborhood of the free boundary
We consider the three-dimensional Euler equations in a domain with a free boundary with no surface tension. We assume that u 0 ∈ H 2.5 + δ is such that c u r l u 0 ∈ H 2 + δ in an arbitrarily small neighborhood of the free boundary, and we use the Lagrangian approach to derive an a priori estimate t...
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| Veröffentlicht in: | Nonlinearity 2023-01, Vol.36 (1), p.636-652 |
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| container_title | Nonlinearity |
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| creator | Kukavica, I Ożański, W S |
| description | We consider the three-dimensional Euler equations in a domain with a free boundary with no surface tension. We assume that
u
0
∈
H
2.5
+
δ
is such that
c
u
r
l
u
0
∈
H
2
+
δ
in an arbitrarily small neighborhood of the free boundary, and we use the Lagrangian approach to derive an a priori estimate that can be used to prove local-in-time existence and uniqueness of solutions under the Rayleigh–Taylor stability condition. |
| doi_str_mv | 10.1088/1361-6544/aca5e3 |
| format | Article |
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u
0
∈
H
2.5
+
δ
is such that
c
u
r
l
u
0
∈
H
2
+
δ
in an arbitrarily small neighborhood of the free boundary, and we use the Lagrangian approach to derive an a priori estimate that can be used to prove local-in-time existence and uniqueness of solutions under the Rayleigh–Taylor stability condition.</description><identifier>ISSN: 0951-7715</identifier><identifier>EISSN: 1361-6544</identifier><identifier>DOI: 10.1088/1361-6544/aca5e3</identifier><identifier>CODEN: NONLE5</identifier><language>eng</language><publisher>IOP Publishing</publisher><subject>35Q31 ; 35R35 ; Euler equations ; free boundary ; Lagrangian coordinates</subject><ispartof>Nonlinearity, 2023-01, Vol.36 (1), p.636-652</ispartof><rights>2022 IOP Publishing Ltd & London Mathematical Society</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c1963-d8f034feff5d629aaf9778555d776be598175d17e9c380958c26f73a534fb4883</citedby><cites>FETCH-LOGICAL-c1963-d8f034feff5d629aaf9778555d776be598175d17e9c380958c26f73a534fb4883</cites><orcidid>0000-0003-1492-0847 ; 0000-0002-9234-2758</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://iopscience.iop.org/article/10.1088/1361-6544/aca5e3/pdf$$EPDF$$P50$$Giop$$H</linktopdf><link.rule.ids>314,780,784,27915,27916,53837,53884</link.rule.ids></links><search><creatorcontrib>Kukavica, I</creatorcontrib><creatorcontrib>Ożański, W S</creatorcontrib><title>Local-in-time existence of a free-surface 3D Euler flow with H 2+δ initial vorticity in a neighborhood of the free boundary</title><title>Nonlinearity</title><addtitle>Non</addtitle><addtitle>Nonlinearity</addtitle><description>We consider the three-dimensional Euler equations in a domain with a free boundary with no surface tension. We assume that
u
0
∈
H
2.5
+
δ
is such that
c
u
r
l
u
0
∈
H
2
+
δ
in an arbitrarily small neighborhood of the free boundary, and we use the Lagrangian approach to derive an a priori estimate that can be used to prove local-in-time existence and uniqueness of solutions under the Rayleigh–Taylor stability condition.</description><subject>35Q31</subject><subject>35R35</subject><subject>Euler equations</subject><subject>free boundary</subject><subject>Lagrangian coordinates</subject><issn>0951-7715</issn><issn>1361-6544</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2023</creationdate><recordtype>article</recordtype><recordid>eNp9kLFOwzAURS0EEqWwM3pgA1M7jmNnRKVQpEosMFuOYxNXqV05KaUSn8V38E04FDEhlvekq3uu3rsAnBN8TbAQE0ILggqW5xOlFTP0AIx-pUMwwiUjiHPCjsFJ1y0xJkRkdATeF0GrFjmPercy0Ly5rjdeGxgsVNBGY1C3iVYlhd7C2aY1Edo2bOHW9Q2cw-zy8wM673qnWvgaYu-063dJSbQ37qWpQmxCqIe8vjHfibAKG1-ruDsFR1a1nTn72WPwfDd7ms7R4vH-YXqzQJqUBUW1sJjm1ljL6iIrlbIl54IxVnNeVIaVgnBWE25KTUV6VOissJwqlqAqF4KOAd7n6hi6Lhor19Gt0gGSYDm0J4eq5FCV3LeXkKs94sJaLsMm-nTgf_aLP-w-eEkLmaxprmtLvwD-R36I</recordid><startdate>20230101</startdate><enddate>20230101</enddate><creator>Kukavica, I</creator><creator>Ożański, W S</creator><general>IOP Publishing</general><scope>AAYXX</scope><scope>CITATION</scope><orcidid>https://orcid.org/0000-0003-1492-0847</orcidid><orcidid>https://orcid.org/0000-0002-9234-2758</orcidid></search><sort><creationdate>20230101</creationdate><title>Local-in-time existence of a free-surface 3D Euler flow with H 2+δ initial vorticity in a neighborhood of the free boundary</title><author>Kukavica, I ; Ożański, W S</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c1963-d8f034feff5d629aaf9778555d776be598175d17e9c380958c26f73a534fb4883</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2023</creationdate><topic>35Q31</topic><topic>35R35</topic><topic>Euler equations</topic><topic>free boundary</topic><topic>Lagrangian coordinates</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Kukavica, I</creatorcontrib><creatorcontrib>Ożański, W S</creatorcontrib><collection>CrossRef</collection><jtitle>Nonlinearity</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Kukavica, I</au><au>Ożański, W S</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Local-in-time existence of a free-surface 3D Euler flow with H 2+δ initial vorticity in a neighborhood of the free boundary</atitle><jtitle>Nonlinearity</jtitle><stitle>Non</stitle><addtitle>Nonlinearity</addtitle><date>2023-01-01</date><risdate>2023</risdate><volume>36</volume><issue>1</issue><spage>636</spage><epage>652</epage><pages>636-652</pages><issn>0951-7715</issn><eissn>1361-6544</eissn><coden>NONLE5</coden><abstract>We consider the three-dimensional Euler equations in a domain with a free boundary with no surface tension. We assume that
u
0
∈
H
2.5
+
δ
is such that
c
u
r
l
u
0
∈
H
2
+
δ
in an arbitrarily small neighborhood of the free boundary, and we use the Lagrangian approach to derive an a priori estimate that can be used to prove local-in-time existence and uniqueness of solutions under the Rayleigh–Taylor stability condition.</abstract><pub>IOP Publishing</pub><doi>10.1088/1361-6544/aca5e3</doi><tpages>17</tpages><orcidid>https://orcid.org/0000-0003-1492-0847</orcidid><orcidid>https://orcid.org/0000-0002-9234-2758</orcidid><oa>free_for_read</oa></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0951-7715 |
| ispartof | Nonlinearity, 2023-01, Vol.36 (1), p.636-652 |
| issn | 0951-7715 1361-6544 |
| language | eng |
| recordid | cdi_crossref_primary_10_1088_1361_6544_aca5e3 |
| source | IOP Publishing Journals; Institute of Physics (IOP) Journals - HEAL-Link |
| subjects | 35Q31 35R35 Euler equations free boundary Lagrangian coordinates |
| title | Local-in-time existence of a free-surface 3D Euler flow with H 2+δ initial vorticity in a neighborhood of the free boundary |
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