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Uniform shear flow via the Boltzmann equation with hard potentials
Renjun Duan, Shuangqian Liu
The motion of rarefied gases for uniform shear flow at the kinetic level is governed by the spatially homogeneous Boltzmann equation with a deformation force. In the paper we study…
Hilbert expansion for kinetic equations with non-relativistic Coulomb collision
Yuanjie Lei, Shuangqian Liu, Qinghua Xiao +1
In this paper, we study the hydrodynamic limits of both the Landau equation and the Vlasov-Maxwell-Landau system in the whole space. Our main purpose is two-fold: the first one is…
The Boltzmann equation for plane Couette flow
Renjun Duan, Shuangqian Liu, Tong Yang
In the paper, we study the plane Couette flow of a rarefied gas between two parallel infinite plates at moving relative to each other with opposite velocities $(\pm αL,0,…
Global mild solutions of the Landau and non-cutoff Boltzmann equations
Renjun Duan, Shuangqian Liu, Shota Sakamoto +1
This paper proves the existence of small-amplitude global-in-time unique mild solutions to both the Landau equation including the Coulomb potential and the Boltzmann equation witho…
Ion-acoustic shock in a collisional plasma
Renjun Duan, Shuangqian Liu, Zhu Zhang
The paper is concerned with the propagation of ion-acoustic shock waves in a collision dominated plasma. We firstly establish the existence and uniqueness of a small-amplitude smoo…
The Boltzmann equation with weakly inhomogeneous data in bounded domain
Yan Guo, Shuangqian Liu
This paper is concerned with the Boltzmann equation with specular reflection boundary condition. We construct a unique global solution and obtain its large time asymptotic behavior…