{"title":"二维各向异性磁bassariard方程的正则性判据","authors":"Dipendra Sharma","doi":"10.4208/JMS.V52N1.19.06","DOIUrl":null,"url":null,"abstract":"In this paper, we study the global regularity issue of two dimensional incompressible magnetic Bénard equations with partial dissipation and magnetic diffusion. It remains open whether the smooth initial data produce solutions that are globally regular in time for all values of the parameters involved in the equations. We present conditional global regularity of the solutions. Moreover, we prove the global regularity for the slightly regularized system. AMS subject classifications: 35Q35, 35B35, 35B65, 76D03","PeriodicalId":43526,"journal":{"name":"数学研究","volume":" ","pages":""},"PeriodicalIF":0.8000,"publicationDate":"2019-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":"{\"title\":\"Regularity Criteria on the 2D Anisotropic Magnetic Bénard Equations\",\"authors\":\"Dipendra Sharma\",\"doi\":\"10.4208/JMS.V52N1.19.06\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper, we study the global regularity issue of two dimensional incompressible magnetic Bénard equations with partial dissipation and magnetic diffusion. It remains open whether the smooth initial data produce solutions that are globally regular in time for all values of the parameters involved in the equations. We present conditional global regularity of the solutions. Moreover, we prove the global regularity for the slightly regularized system. AMS subject classifications: 35Q35, 35B35, 35B65, 76D03\",\"PeriodicalId\":43526,\"journal\":{\"name\":\"数学研究\",\"volume\":\" \",\"pages\":\"\"},\"PeriodicalIF\":0.8000,\"publicationDate\":\"2019-06-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"3\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"数学研究\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.4208/JMS.V52N1.19.06\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"数学研究","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.4208/JMS.V52N1.19.06","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Regularity Criteria on the 2D Anisotropic Magnetic Bénard Equations
In this paper, we study the global regularity issue of two dimensional incompressible magnetic Bénard equations with partial dissipation and magnetic diffusion. It remains open whether the smooth initial data produce solutions that are globally regular in time for all values of the parameters involved in the equations. We present conditional global regularity of the solutions. Moreover, we prove the global regularity for the slightly regularized system. AMS subject classifications: 35Q35, 35B35, 35B65, 76D03
期刊介绍:
Journal of Mathematical Study (JMS) is a comprehensive mathematical journal published jointly by Global Science Press and Xiamen University. It publishes original research and survey papers, in English, of high scientific value in all major fields of mathematics, including pure mathematics, applied mathematics, operational research, and computational mathematics.