Global classical solutions for 3D compressible magneto-micropolar fluids without resistivity and spin viscosity in a strip domain  

作　　者：Zefu Feng Guangyi Hong Changjiang Zhu 

机构地区：[1]School of Mathematical Sciences,Chongqing Normal University,Chongqing 401331,China [2]School of Mathematics,South China University of Technology,Guangzhou 510641,China

出　　处：《Science China Mathematics》2024年第11期2485-2514,共30页中国科学（数学英文版）

基　　金：supported by National Natural Science Foundation of China(Grant No.12101095);the Science and Technology Research Program of Chongqing Municipal Education Commission(Grant No.KJQN202100517);the Research Project of Chongqing Education Commission(Grant No.CXQT21014);the Natural Science Foundation of Chongqing(Grant No.cstc2021jcyj-msxm X0224);the Grant of Chongqing Young Experts’Workshop;supported by National Natural Science Foundation of China(Grant No.12201221);the Guangdong Basic and Applied Basic Research Foundation(Grant No.2021A1515111038);Changjiang Zhu was supported by National Natural Science Foundation of China(Grant Nos.12171160 and 11831003);the Guangdong Provincial Key Laboratory of Human Digital Twin(Grant No.2022B1212010004)。

摘　　要：In this paper,we consider 3D compressible magneto-micropolar fluids without resistivity and spin viscosity in a strip domain.The prominent character of the governing model is the presence of the microstructure,a linear coupling structure involving derivatives of the velocity fields,which along with the lack of spin viscosity brings several challenges to the analysis.By exploiting the two-tier energy method developed in Guo and Tice(Arch Ration Mech Anal,2013),we prove the global existence of classical solutions to the governing model around a uniform magnetic field that is non-parallel to the horizontal boundary.Moreover,we show that the solution converges to the steady state at an almost exponential rate as time goes to infinity.One of the main ingredients in our analysis,compared with previous works on micropolar fluids,is that we deal with the microstructure by establishing some delicate estimates based on the analysis of the div-curl decomposition,and the coupling between the fluid velocity and the vorticity of angular velocity.

关 键 词：magneto-micropolar fluids COMPRESSIBLE global existence large-time behavior 

分 类 号：O373[理学—流体力学]