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A non-steady system with friction boundary conditions for flow of heat-conducting incompressible viscous fluids
Kim, Tujin1; Cao, Daomin2,3
2020-04-01
Source PublicationJOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
ISSN0022-247X
Volume484Issue:1Pages:42
AbstractIn this paper we are concerned with a non-steady system for motion of incompressible viscous Newtonian heat-conducting fluids under mixed boundary conditions. The boundary conditions for fluid may include Tresca slip, leak and one-sided leak conditions based on total stress, velocity, total pressure, rotation, total stress together and the conditions for temperature may include Dirichlet, Neumann and Robin conditions together. Relying on the relations among strain, rotation, normal derivative of velocity and shape of boundary surface, we get variational formulation. The formulation consists of a variational inequality for velocity due to the boundary conditions of friction type and a variational equation for temperature. We first study existence, estimation and relative compactness of solutions to an approximate equation. By passing to limits as the parameter for approximation goes to zero, we get existence of a solution with "defect measure" for temperature. C) 2019 Published by Elsevier Inc.
KeywordHeat-conducting fluids Dissipative heating Mixed boundary conditions Tresca slip Leak boundary conditions Pressure boundary condition
DOI10.1016/j.jmaa.2019.123676
Indexed BySCI
Language英语
Funding ProjectGuangzhou University, P. R. China ; NSFC[11771469] ; NSFC[11688101] ; Key Laboratory of Random Complex Structures and Data Science, Chinese Academy of Sciences[2008DP173182]
WOS Research AreaMathematics
WOS SubjectMathematics, Applied ; Mathematics
WOS IDWOS:000508488800033
PublisherACADEMIC PRESS INC ELSEVIER SCIENCE
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Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/50568
Collection中国科学院数学与系统科学研究院
Corresponding AuthorKim, Tujin
Affiliation1.Acad Sci, Inst Math, Pyongyang, North Korea
2.Chinese Acad Sci, AMSS, Inst Appl Math, Beijing 100190, Peoples R China
3.Guangzhou Univ, Sch Math & Informat Sci, Guangzhou 510405, Guangdong, Peoples R China
Recommended Citation
GB/T 7714
Kim, Tujin,Cao, Daomin. A non-steady system with friction boundary conditions for flow of heat-conducting incompressible viscous fluids[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS,2020,484(1):42.
APA Kim, Tujin,&Cao, Daomin.(2020).A non-steady system with friction boundary conditions for flow of heat-conducting incompressible viscous fluids.JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS,484(1),42.
MLA Kim, Tujin,et al."A non-steady system with friction boundary conditions for flow of heat-conducting incompressible viscous fluids".JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS 484.1(2020):42.
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