80 citations · 211 across the 17 of their papers we have counts for
18 papers
Global mild solution with polynomial tail for the Boltzmann equation in the whole space
Renjun Duan, Zongguang Li, Shuangqian Liu
We are concerned with the Cauchy problem on the Boltzmann equation in the whole space. The goal is to construct global-in-time bounded mild solutions near Maxwellians with the pert…
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…
Heat transfer problem for the Boltzmann equation in a channel with diffusive boundary condition
Renjun Duan, Shuangqian Liu, Tong Yang +1
In this paper, we study the 1D steady Boltzmann flow in a channel. The walls of the channel are assumed to have vanishing velocity and given temperatures and . This prob…
On smooth solutions to the thermostated Boltzmann equation with deformation
Renjun Duan, Shuangqian Liu
This paper concerns a kinetic model of the thermostated Boltzmann equation with a linear deformation force described by a constant matrix. The collision kernel under consideration…
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,…
The Boltzmann equation for uniform shear flow
Renjun Duan, Shuangqian Liu
The uniform shear flow for the rarefied gas is governed by the time-dependent spatially homogeneous Boltzmann equation with a linear shear force. The main feature of such flow is t…
A Note On Free Boundary Minimal Annulus
Shuangqi Liu, Zuhuan Yu
In this note we investigate free boundary minimal surfaces in the Euclidean 3-space, and by using holomorphic techniques developed by Fraser and Schoen we prove that the free bound…
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…
Incompressible hydrodynamic approximation with viscous heating to the Boltzmann equation
Yan Guo, Shuangqian Liu
The incompressible Navier-Stokes-Fourier system with viscous heating was first derived from the Boltzmann equation in the form of the diffusive scaling by Bardos-Levermore-Ukai-Yan…
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…
The initial boundary value problem for the Boltzmann equation with soft potential
Shuangqian Liu, Xiongfeng Yang
Boundary effects are central to the dynamics of the dilute particles governed by Boltzmann equation. In this paper, we study both the diffuse reflection and the specular reflection…
The Vlasov-Poisson-Boltzmann system for a disparate mass binary mixture
Renjun Duan, Shuangqian Liu
The Vlasov-Poisson-Boltzmann system is often used to govern the motion of plasmas consisting of electrons and ions with disparate masses when collisions of charged particles are de…
Stability of contact discontinuity for the Navier-Stokes-Poisson system with free boundary
Shuangqian Liu, Haiyan Yin, Changjiang Zhu
This paper is concerned with the study of the nonlinear stability of the contact discontinuity of the Navier-Stokes-Poisson system with free boundary in the case where the electron…
Stability of rarefaction waves of the Navier-Stokes-Poisson system
Renjun Duan, Shuangqian Liu
In the paper we are concerned with the large time behavior of solutions to the one-dimensional Navier-Stokes-Poisson system in the case when the potential function of the self-cons…
Global well-posedness in spatially critical Besov space for the Boltzmann equation
Renjun Duan, Shuangqian Liu, Jiang Xu
The unique global strong solution in the Chemin-Lerner type space to the Cauchy problem on the Boltzmann equation for hard potentials is constructed in perturbation framework. Such…
The Vlasov-Poisson-Boltzmann system without angular cutoff
Renjun Duan, Shuangqian Liu
This paper is concerned with the Vlasov-Poisson-Boltzmann system for plasma particles of two species in three space dimensions. The Boltzmann collision kernel is assumed to be angu…