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This work gathers new results concerning the semigeostrophic equations: existence and stability of measure\u2010valued solutions, existence and uniqueness of solutions under certain continuity conditions for the density, and convergence to the incompressible Euler equations.<\/jats:p>","DOI":"10.1137\/050629070","type":"journal-article","created":{"date-parts":[[2006,8,24]],"date-time":"2006-08-24T15:31:03Z","timestamp":1156433463000},"page":"795-823","source":"Crossref","is-referenced-by-count":45,"title":["A Fully Nonlinear Version of the Incompressible Euler Equations: The Semigeostrophic System"],"prefix":"10.1137","volume":"38","author":[{"given":"G.","family":"Loeper","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2006,8,7]]},"reference":[{"key":"R1","doi-asserted-by":"publisher","DOI":"10.1137\/S0036139995294111"},{"key":"R2","doi-asserted-by":"publisher","DOI":"10.1007\/s002110050002"},{"key":"R3","doi-asserted-by":"publisher","DOI":"10.1002\/cpa.3160440402"},{"key":"R4","doi-asserted-by":"publisher","DOI":"10.1080\/03605300008821529"},{"key":"R5","doi-asserted-by":"publisher","DOI":"10.1007\/s00039-004-0488-1"},{"key":"R6","doi-asserted-by":"publisher","DOI":"10.2307\/1971510"},{"key":"R7","doi-asserted-by":"publisher","DOI":"10.2307\/1971509"},{"key":"R8","doi-asserted-by":"publisher","DOI":"10.1090\/S0894-0347-1992-1124980-8"},{"key":"R9","doi-asserted-by":"publisher","DOI":"10.1016\/S0764-4442(00)88593-6"},{"key":"R10","doi-asserted-by":"publisher","DOI":"10.1007\/s002050000124"},{"key":"R11","doi-asserted-by":"publisher","DOI":"10.1007\/s00205-003-0245-x"},{"key":"R12","doi-asserted-by":"publisher","DOI":"10.1175\/1520-0469(1989)046<2684:POTLSE>2.0.CO;2"},{"key":"R13","doi-asserted-by":"crossref","unstructured":"C. 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Mat."}],"container-title":["SIAM Journal on Mathematical Analysis"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/050629070","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T13:28:16Z","timestamp":1787318896000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/050629070"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2006,1]]},"references-count":26,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2006,1]]}},"alternative-id":["10.1137\/050629070"],"URL":"https:\/\/doi.org\/10.1137\/050629070","relation":{},"ISSN":["0036-1410","1095-7154"],"issn-type":[{"value":"0036-1410","type":"print"},{"value":"1095-7154","type":"electronic"}],"subject":[],"published":{"date-parts":[[2006,1]]}}}