{"title":"允许真空的二维还原引力二层半系统弱解的能量相等性","authors":"Xiang Ji, Fan Wu, Yanping Gao","doi":"10.1002/mma.10380","DOIUrl":null,"url":null,"abstract":"The energy conservation problem for the reduced‐gravity two‐and‐a‐half layer model remains a challenging open problem, with several recent contributions addressing various aspects of it. In this paper, we establish sufficient conditions on the regularity of weak solutions that guarantee energy conservation even in the presence of a vacuum. Our theorem corresponds to an improvement of some recent results on this problem and contains some well‐known results as a particular case.","PeriodicalId":2,"journal":{"name":"ACS Applied Bio Materials","volume":null,"pages":null},"PeriodicalIF":4.6000,"publicationDate":"2024-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Energy equality of weak solutions of the 2D reduced‐gravity two‐and‐a‐half layer system allowing vacuum\",\"authors\":\"Xiang Ji, Fan Wu, Yanping Gao\",\"doi\":\"10.1002/mma.10380\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The energy conservation problem for the reduced‐gravity two‐and‐a‐half layer model remains a challenging open problem, with several recent contributions addressing various aspects of it. In this paper, we establish sufficient conditions on the regularity of weak solutions that guarantee energy conservation even in the presence of a vacuum. Our theorem corresponds to an improvement of some recent results on this problem and contains some well‐known results as a particular case.\",\"PeriodicalId\":2,\"journal\":{\"name\":\"ACS Applied Bio Materials\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":4.6000,\"publicationDate\":\"2024-07-31\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"ACS Applied Bio Materials\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1002/mma.10380\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATERIALS SCIENCE, BIOMATERIALS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"ACS Applied Bio Materials","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1002/mma.10380","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATERIALS SCIENCE, BIOMATERIALS","Score":null,"Total":0}
Energy equality of weak solutions of the 2D reduced‐gravity two‐and‐a‐half layer system allowing vacuum
The energy conservation problem for the reduced‐gravity two‐and‐a‐half layer model remains a challenging open problem, with several recent contributions addressing various aspects of it. In this paper, we establish sufficient conditions on the regularity of weak solutions that guarantee energy conservation even in the presence of a vacuum. Our theorem corresponds to an improvement of some recent results on this problem and contains some well‐known results as a particular case.
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