Global Weak Solutions for Compressible Navier-Stokes-Vlasov-Fokker-Planck System  

作　　者：Hai-Liang Li Ling-Yun Shou 

机构地区：[1]School of Mathematical Sciences,Academy for Multidisciplinary Studies,Capital Normal University,Beijing 100048,P.R.China

出　　处：《Communications in Mathematical Research》2023年第1期136-172,共37页数学研究通讯（英文版）

基　　金：The research of the paper is supported by National Natural Science Foundation of China(Nos.11931010,11671384,11871047);by the key research project of Academy for Multidisciplinary Studies,Capital Normal University,and by the Capacity Building for Sci-Tech Innovation-Fundamental Scientific Research Funds(No.007/20530290068).

摘　　要：The one-dimensional compressible Navier-Stokes-Vlasov-Fokker-Planck system with density-dependent viscosity and drag force coefficients is investigated in the present paper.The existence,uniqueness,and regularity of global weak solution to the initial value problem for general initial data are established in spatial periodic domain.Moreover,the iong time behavior of the weak solution is analyzed.It is shown that as the time grows,the distri-bution function of the particles converges to the global Maxwellian,and both the fluid velocity and the macroscopic velocity of the particles converge to the same speed.

关 键 词：Fluid-particle model compressible Navier-Stokes-Vlasov-Fokker-Planck hy-poellipticity global existence large time behavior 

分 类 号：O359[理学—流体力学]