A non-steady system with friction boundary conditions for flow of heat-conducting incompressible viscous fluids

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:484

Article

Kim, Tujin¹  Cao, Daomin^2,3 

[1] 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

关键词: Heat-conducting fluids;    Dissipative heating;    Mixed boundary conditions;    Tresca slip;    Leak boundary conditions;    Pressure boundary condition;   

DOI  :  10.1016/j.jmaa.2019.123676

来源: Elsevier

【 摘 要 】

In 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.

【 授权许可】

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