{"title":"紧流形上的伪微分计算和非线性演化方程","authors":"Mohammed Aassila","doi":"10.1016/S0764-4442(01)02106-1","DOIUrl":null,"url":null,"abstract":"<div><p>By using the pseudo-differential and para-differential calculus introduced by J.-M. Bony [1], we study the incompressible isotropic Navier–Stokes equations. We prove the short-time existence and uniqueness of solutions for arbitrary data with supercritical regularity. We exploit pseudo-differential calculus to extend the analysis to compact Riemannian manifolds.</p></div>","PeriodicalId":100300,"journal":{"name":"Comptes Rendus de l'Académie des Sciences - Series I - Mathematics","volume":"333 7","pages":"Pages 617-622"},"PeriodicalIF":0.0000,"publicationDate":"2001-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/S0764-4442(01)02106-1","citationCount":"4","resultStr":"{\"title\":\"Calcul pseudo-différentiel et équations d'évolution non linéaires sur les variétés compactes\",\"authors\":\"Mohammed Aassila\",\"doi\":\"10.1016/S0764-4442(01)02106-1\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>By using the pseudo-differential and para-differential calculus introduced by J.-M. Bony [1], we study the incompressible isotropic Navier–Stokes equations. We prove the short-time existence and uniqueness of solutions for arbitrary data with supercritical regularity. We exploit pseudo-differential calculus to extend the analysis to compact Riemannian manifolds.</p></div>\",\"PeriodicalId\":100300,\"journal\":{\"name\":\"Comptes Rendus de l'Académie des Sciences - Series I - Mathematics\",\"volume\":\"333 7\",\"pages\":\"Pages 617-622\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2001-10-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1016/S0764-4442(01)02106-1\",\"citationCount\":\"4\",\"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/S0764444201021061\",\"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/S0764444201021061","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Calcul pseudo-différentiel et équations d'évolution non linéaires sur les variétés compactes
By using the pseudo-differential and para-differential calculus introduced by J.-M. Bony [1], we study the incompressible isotropic Navier–Stokes equations. We prove the short-time existence and uniqueness of solutions for arbitrary data with supercritical regularity. We exploit pseudo-differential calculus to extend the analysis to compact Riemannian manifolds.
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