{"title":"Energy Conservation of the 4 D Incompressible Navier-Stokes Equations","authors":"WANG Bin, ZHOU Yanping, BIE Qunyi","doi":"10.21656/1000-0887.430370","DOIUrl":null,"url":null,"abstract":"The energy conservation of 4D incompressible Navier-Stokes equations was studied. In the case of a singular set with a dimension number less than 4 for the Leray-Hopf weak solution (suitable weak solution), the <inline-formula><tex-math id=\"M2\">\\begin{document}$L^q\\left([0, T] ; L^p\\left(\\mathbb{R}^4\\right)\\right)$\\end{document}</tex-math></inline-formula> condition in the 4D space was obtained based on Wu's partial regularity results about the 4D incompressible Navier-Stokes equations, to ensure the energy conservation.","PeriodicalId":8341,"journal":{"name":"Applied Mathematics and Mechanics","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Applied Mathematics and Mechanics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.21656/1000-0887.430370","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"Mathematics","Score":null,"Total":0}
引用次数: 0
Abstract
The energy conservation of 4D incompressible Navier-Stokes equations was studied. In the case of a singular set with a dimension number less than 4 for the Leray-Hopf weak solution (suitable weak solution), the \begin{document}$L^q\left([0, T] ; L^p\left(\mathbb{R}^4\right)\right)$\end{document} condition in the 4D space was obtained based on Wu's partial regularity results about the 4D incompressible Navier-Stokes equations, to ensure the energy conservation.
The energy conservation of 4D incompressible Navier-Stokes equations was studied. In the case of a singular set with a dimension number less than 4 for the Leray-Hopf weak solution (suitable weak solution), the \begin{document}$L^q\left([0, T] ; L^p\left(\mathbb{R}^4\right)\right)$\end{document} condition in the 4D space was obtained based on Wu's partial regularity results about the 4D incompressible Navier-Stokes equations, to ensure the energy conservation.