{"title":"玻尔兹曼方程的纳维-斯托克斯极限","authors":"François Golse , Laure Saint-Raymond","doi":"10.1016/S0764-4442(01)02136-X","DOIUrl":null,"url":null,"abstract":"<div><p>Appropriately scaled families of DiPerna–Lions renormalized solutions of the Boltzmann equation are shown to have fluctuations whose limit points (in the weak L<sup>1</sup> topology) are governed by a Leray solution of the limiting Navier–Stokes equations. This completes the arguments in Bardos–Golse–Levermore [Commun. on Pure and Appl. Math. 46 (5) (1993) 667–753] for the steady case, extended by Lions–Masmoudi [Arch. Ration. Mech. Anal. 158 (3) (2001) 173–193] to the time-dependent case.</p></div>","PeriodicalId":100300,"journal":{"name":"Comptes Rendus de l'Académie des Sciences - Series I - Mathematics","volume":"333 9","pages":"Pages 897-902"},"PeriodicalIF":0.0000,"publicationDate":"2001-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/S0764-4442(01)02136-X","citationCount":"16","resultStr":"{\"title\":\"The Navier–Stokes limit for the Boltzmann equation\",\"authors\":\"François Golse , Laure Saint-Raymond\",\"doi\":\"10.1016/S0764-4442(01)02136-X\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>Appropriately scaled families of DiPerna–Lions renormalized solutions of the Boltzmann equation are shown to have fluctuations whose limit points (in the weak L<sup>1</sup> topology) are governed by a Leray solution of the limiting Navier–Stokes equations. This completes the arguments in Bardos–Golse–Levermore [Commun. on Pure and Appl. Math. 46 (5) (1993) 667–753] for the steady case, extended by Lions–Masmoudi [Arch. Ration. Mech. Anal. 158 (3) (2001) 173–193] to the time-dependent case.</p></div>\",\"PeriodicalId\":100300,\"journal\":{\"name\":\"Comptes Rendus de l'Académie des Sciences - Series I - Mathematics\",\"volume\":\"333 9\",\"pages\":\"Pages 897-902\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2001-11-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1016/S0764-4442(01)02136-X\",\"citationCount\":\"16\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Comptes Rendus de l'Académie des Sciences - Series I - Mathematics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S076444420102136X\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Comptes Rendus de l'Académie des Sciences - Series I - Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S076444420102136X","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
The Navier–Stokes limit for the Boltzmann equation
Appropriately scaled families of DiPerna–Lions renormalized solutions of the Boltzmann equation are shown to have fluctuations whose limit points (in the weak L1 topology) are governed by a Leray solution of the limiting Navier–Stokes equations. This completes the arguments in Bardos–Golse–Levermore [Commun. on Pure and Appl. Math. 46 (5) (1993) 667–753] for the steady case, extended by Lions–Masmoudi [Arch. Ration. Mech. Anal. 158 (3) (2001) 173–193] to the time-dependent case.
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