# 学术讲座 Lecture

## 【19.9.22 16:00-16:45】学术报告---姚磊教授

2019-09-16 16:33:37 来源：学术报告---姚磊教授 点击： 收藏本文

We study the hydrodynamic limit of weak solutions to the compressible Navier-Stokes-Vlasov equations without diffusive term in one dimension. This work extends in some sense the previous work, [Mellet and Vasseur, Comm. Math. Phys., 281(2008), 573-596], which provided the hydrodynamic limit of weak solutions to the  Vlasov-Fokker-Planck/compressible Navier-Stokes systems in three dimensions with $\frac{3}{2}<\gamma<2$ (where the pressure $p(\rho)=\mathbb{A}\rho^{\gamma}$).  In this study, we improve the results by taking advantage of the one space dimension. More precisely, we obtain the hydrodynamic limit for 1D compressible Navier-Stokes-Vlasov equations. The proof relies on a relative entropy method to obtain the corresponding strong convergence of the density of the fluid.

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