34 citations · 52 across the 9 of their papers we have counts for
10 papers
Shock profiles for the cutoff Boltzmann equation of a binary gas mixture
Renjun Duan, Zongguang Li, Zhu Zhang
We prove the existence of small-amplitude traveling shock profiles for the one-dimensional Boltzmann equation of a binary gas mixture with angular cutoff potentials in the full ran…
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…
Linear instability analysis on compressible Navier-Stokes equations with strong boundary layer
Tong Yang, Zhu Zhang
It is a classical problem in fluid dynamics about the stability and instability of different hydrodynamic patterns in various physical settings, in particular in the high Reynolds…
Analysis on Tollmien-Schlichting wave in the Prandtl-Hartmann Regime
Cheng-Jie Liu, Tong Yang, Zhu Zhang
In this paper, we study the instability induced by the Tollmien-Schlichting wave governed by the MHD system in the Prandtl-Hartmann regime. The interaction of the inviscid mode and…
Validity of Prandtl expansions for steady MHD in the Sobolev framework
Cheng-Jie Liu, Tong Yang, Zhu Zhang
This paper is concerned with the vanishing viscosity and magnetic resistivity limit for the two-dimensional steady incompressible MHD system on the half plane with no-slip boundary…
Solutions to a moving boundary problem on the Boltzmann equation
Renjun Duan, Zhu Zhang
Motivated by the numerical investigation by Aoki et al. [1], we study a rarefied gas flow between two parallel infinite plates of the same temperature governed by the Boltzmann equ…
The Boltzmann equation with time-periodic boundary temperature
Renjun Duan, Yong Wang, Zhu Zhang
This paper is concerned with the boundary-value problem on the Boltzmann equation in bounded domains with diffuse-reflection boundary where the boundary temperature is time-periodi…
Effects of soft interaction and non-isothermal boundary upon long-time dynamics of rarefied gas
Renjun Duan, Feimin Huang, Yong Wang +1
In the paper, assuming that the motion of rarefied gases in a bounded domain is governed by the angular cutoff Boltzmann equation with diffuse reflection boundary, we study the eff…
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…
Instability in a Vlasov-Fokker-Planck binary mixture
Zhu Zhang
This paper is concerned with a kinetic model of a Vlasov-Fokker-Planck system used to describe the evolution of two species of particles interacting through a potential and a therm…