Global Weak Solutions for Compressible Navier-Stokes-Vlasov-Fokker-Planck System (Communications in Mathematical Research, 2022)
The one-dimensional compressible Navier-Stokes-Vlasov-Fokker-Planck system with density-dependent viscosity and drag force coefficients isinvestigated in the present paper. The existence, uniqueness, and regularityof global weak solution to the initial value problem for general initial data areestablished in spatial periodic domain. Moreover, the long time behavior ofthe weak solution is analyzed. It is shown that as the time grows, the distribution function of the particles converges to the global Maxwellian, and boththe fluid velocity and the macroscopic velocity of the particles converge to thesame speed.