TY - JOUR
T1 - Global Weak Solutions for Compressible Navier-Stokes-Vlasov-Fokker-Planck System
AU - Li , Hai-Liang
AU - Shou , Ling-Yun
JO - Communications in Mathematical Research 
VL - 1
SP - 136
EP - 172
PY - 2022
DA - 2022/10
SN - 39
DO - http://doi.org/10.4208/cmr.2021-0039
UR - https://global-sci.org/intro/article_detail/cmr/21081.html
KW - Fluid-particle model, compressible Navier-Stokes-Vlasov-Fokker-Planck, hypoellipticity, global existence, large time behavior.
AB - <p style="text-align: justify;">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.</p>