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 g...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.展开更多
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 g...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 long time behavior of the weak solution is analyzed.It is shown that as the time grows,the distribution 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.展开更多
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).
文摘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.
基金supported by National Natural Science Foundation of China(Nos.11931010,11671384,11871047)by the key research project of Academy for Multidisciplinary Studies,Capital Normal Universityby the Capacity Building for Sci-Tech Innovation-Fundamental Scientific Research Funds(No.007/20530290068).
文摘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 long time behavior of the weak solution is analyzed.It is shown that as the time grows,the distribution 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.
