From the Nash–Kuiper theorem of isometric embeddings to the Euler equations for steady fluid motions: Analogues, examples, and extensions
Direct linkages between regular or irregular isometric embeddings of surfaces and steady compressible or incompressible fluid dynamics are investigated in this paper. For a surface (M, g) isometrically embedded in R3, we construct a mapping that sends the second fundamental form of the embedding to...
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| Veröffentlicht in: | Journal of mathematical physics 2023-01, Vol.64 (1), Article Paper No. 011511, 29 |
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| creator | Li, Siran Slemrod, Marshall |
| description | Direct linkages between regular or irregular isometric embeddings of surfaces and steady compressible or incompressible fluid dynamics are investigated in this paper. For a surface (M, g) isometrically embedded in R3, we construct a mapping that sends the second fundamental form of the embedding to the density, velocity, and pressure of steady fluid flows on (M, g). From a Partial Differential Equations perspective, this mapping sends solutions to the Gauss–Codazzi equations to the steady Euler equations. Several families of special solutions of physical or geometrical significance are studied in detail, including the Chaplygin gas on standard and flat tori as well as the irregular isometric embeddings of the flat torus. We also discuss tentative extensions to multiple dimensions. |
| doi_str_mv | 10.1063/5.0100212 |
| format | Article |
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We also discuss tentative extensions to multiple dimensions.</description><subject>Chaplygin gas</subject><subject>Compressibility</subject><subject>Embedding</subject><subject>Euler-Lagrange equation</subject><subject>Eulers equations</subject><subject>Fluid dynamics</subject><subject>Fluid flow</subject><subject>Incompressible flow</subject><subject>Incompressible fluids</subject><subject>Mapping</subject><subject>Mathematical analysis</subject><subject>Partial differential equations</subject><subject>Physics</subject><subject>Toruses</subject><issn>0022-2488</issn><issn>1089-7658</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2023</creationdate><recordtype>article</recordtype><recordid>eNp9kMtKxDAUhoMoOF4WvkHAlWKdJG3S1N0g3nDQja5LJj0dI23TSVLRnXuXvqFPYucigqirc_v-n8OP0B4lx5SIeMiPCSWEUbaGBpTILEoFl-to0O9YxBIpN9GW94-EUCqTZIDezp2tcXgAfKP8w8fr-3VnWnDzjXVQY1ti420NwRmNoZ5AUZhm6nGwC9FZV_UwzDoVjG08Lq3DPoAqXnBZdabAtV0cTvCoUZWdduCPMDyruq3mnWqKfgrQ-Dm0gzZKVXnYXdVtdH9-dnd6GY1vL65OR-NIx4KFSKdxmepEAOcQM6oFzXQqqSICUply4CCoKGMuCI_lZMILohXlk4RlnGWpFPE22l_6ts7O-o9C_mg71__nc5aKLOkDlKSnDpaUdtZ7B2XeOlMr95JTks-zznm-yrpnhz9YbcIikuCUqX5VHC4V_ov81_5P-Mm6bzBvizL-BLaAnfQ</recordid><startdate>20230101</startdate><enddate>20230101</enddate><creator>Li, Siran</creator><creator>Slemrod, Marshall</creator><general>American Institute of Physics</general><scope>AAYXX</scope><scope>CITATION</scope><scope>7U5</scope><scope>8FD</scope><scope>H8D</scope><scope>JQ2</scope><scope>L7M</scope><orcidid>https://orcid.org/0000-0003-4283-273X</orcidid><orcidid>https://orcid.org/0000-0002-0514-9467</orcidid></search><sort><creationdate>20230101</creationdate><title>From the Nash–Kuiper theorem of isometric embeddings to the Euler equations for steady fluid motions: Analogues, examples, and extensions</title><author>Li, Siran ; Slemrod, Marshall</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c362t-c73f7c46e55e321c619c781a06e7875e5e616f3560538bb5d0ca15b4295297863</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2023</creationdate><topic>Chaplygin gas</topic><topic>Compressibility</topic><topic>Embedding</topic><topic>Euler-Lagrange equation</topic><topic>Eulers equations</topic><topic>Fluid dynamics</topic><topic>Fluid flow</topic><topic>Incompressible flow</topic><topic>Incompressible fluids</topic><topic>Mapping</topic><topic>Mathematical analysis</topic><topic>Partial differential equations</topic><topic>Physics</topic><topic>Toruses</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Li, Siran</creatorcontrib><creatorcontrib>Slemrod, Marshall</creatorcontrib><collection>CrossRef</collection><collection>Solid State and Superconductivity Abstracts</collection><collection>Technology Research Database</collection><collection>Aerospace Database</collection><collection>ProQuest Computer Science Collection</collection><collection>Advanced Technologies Database with Aerospace</collection><jtitle>Journal of mathematical physics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Li, Siran</au><au>Slemrod, Marshall</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>From the Nash–Kuiper theorem of isometric embeddings to the Euler equations for steady fluid motions: Analogues, examples, and extensions</atitle><jtitle>Journal of mathematical physics</jtitle><date>2023-01-01</date><risdate>2023</risdate><volume>64</volume><issue>1</issue><artnum>Paper No. 011511, 29</artnum><issn>0022-2488</issn><eissn>1089-7658</eissn><coden>JMAPAQ</coden><abstract>Direct linkages between regular or irregular isometric embeddings of surfaces and steady compressible or incompressible fluid dynamics are investigated in this paper. 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| fulltext | fulltext |
| identifier | ISSN: 0022-2488 |
| ispartof | Journal of mathematical physics, 2023-01, Vol.64 (1), Article Paper No. 011511, 29 |
| issn | 0022-2488 1089-7658 |
| language | eng |
| recordid | cdi_scitation_primary_10_1063_5_0100212 |
| source | AIP Journals Complete; Alma/SFX Local Collection |
| subjects | Chaplygin gas Compressibility Embedding Euler-Lagrange equation Eulers equations Fluid dynamics Fluid flow Incompressible flow Incompressible fluids Mapping Mathematical analysis Partial differential equations Physics Toruses |
| title | From the Nash–Kuiper theorem of isometric embeddings to the Euler equations for steady fluid motions: Analogues, examples, and extensions |
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