Special Session 25: Recent Progress on Mathematical Analysis of PDEs Arising in Fluid Dynamics

Hydrodynamic limit for compressible Navier-Stokes-Vlasov equations
Lei Yao
Northwestern Polytechnical University
Peoples Rep of China
Co-Author(s):    Yunfei Su; Lei Yao
Abstract:
We study the hydrodynamic limit of weak solutions to compressible Navier-Stokes-Vlasov equations in one dimension bounded domain. Due to the absence of dissipation terms in particle equation, it is difficult to study this problem. We take advantage of compactness result in one space dimension to obtain the convergence of macroscopic density of the particles in $C([0,T];H^{-1})$. The proof relies on relative entropy method to obtain the corresponding strong convergence of fluid density. At last, we give a recent result about hydrodynamic limit for multidimensional compressible Navier-Stokes-Vlasov-Poisson equations with local alignment force.