{"title":"三维同向旋转贝里斯-爱德华兹系统合适弱解的闵科夫斯基维度","authors":"Zhongbao Zuo","doi":"10.1007/s00033-024-02284-x","DOIUrl":null,"url":null,"abstract":"<p>In this paper, we study the possible singular points of suitable weak solutions to the 3D co-rotational Beris-Edwards system. Inspired by the work of He et al. (J. Nonlinear Sci. 29:2681–2698, 2019) and Wang et al. (Nonlinearity 32:4817–4833, 2019) for Navier–Stokes equations, we established a new partial regularity criteria for co-rotational Beris-Edwards system. As an application, we prove the known Minkowski dimension of the potential interior singular set of suitable weak solutions of the co-rotational Beris-Edwards system is <span>\\(\\frac{7}{6}(\\approx 1.167)\\)</span>.</p>","PeriodicalId":501481,"journal":{"name":"Zeitschrift für angewandte Mathematik und Physik","volume":"41 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-07-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"The Minkowski dimension of suitable weak solutions of the 3D co-rotational Beris-Edwards system\",\"authors\":\"Zhongbao Zuo\",\"doi\":\"10.1007/s00033-024-02284-x\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>In this paper, we study the possible singular points of suitable weak solutions to the 3D co-rotational Beris-Edwards system. Inspired by the work of He et al. (J. Nonlinear Sci. 29:2681–2698, 2019) and Wang et al. (Nonlinearity 32:4817–4833, 2019) for Navier–Stokes equations, we established a new partial regularity criteria for co-rotational Beris-Edwards system. As an application, we prove the known Minkowski dimension of the potential interior singular set of suitable weak solutions of the co-rotational Beris-Edwards system is <span>\\\\(\\\\frac{7}{6}(\\\\approx 1.167)\\\\)</span>.</p>\",\"PeriodicalId\":501481,\"journal\":{\"name\":\"Zeitschrift für angewandte Mathematik und Physik\",\"volume\":\"41 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-07-14\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Zeitschrift für angewandte Mathematik und Physik\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1007/s00033-024-02284-x\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Zeitschrift für angewandte Mathematik und Physik","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1007/s00033-024-02284-x","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
The Minkowski dimension of suitable weak solutions of the 3D co-rotational Beris-Edwards system
In this paper, we study the possible singular points of suitable weak solutions to the 3D co-rotational Beris-Edwards system. Inspired by the work of He et al. (J. Nonlinear Sci. 29:2681–2698, 2019) and Wang et al. (Nonlinearity 32:4817–4833, 2019) for Navier–Stokes equations, we established a new partial regularity criteria for co-rotational Beris-Edwards system. As an application, we prove the known Minkowski dimension of the potential interior singular set of suitable weak solutions of the co-rotational Beris-Edwards system is \(\frac{7}{6}(\approx 1.167)\).
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