5 citations · 7 across the 10 of their papers we have counts for
10 papers
On a free boundary problem of the Boltzmann equation
Shengchuang Chang, Renjun Duan, Shuangqian Liu
This paper studies a free boundary problem for the Boltzmann equation that models the interaction of rarefied gas with a moving wall---a classical piston problem in kinetic theory.…
Time-periodic solutions of the Boltzmann equation with soft potentials in
Yuanjie Lei, Shuangqian Liu, Jiaying Zhang +1
We establish the existence of time-periodic solutions to the Boltzmann equation for the full range of soft potentials and prove their global stability. The proof relies on refined…
The Boltzmann equation in an infinite layer: spectrum and asymptotics toward the heat equation
Hongxu Chen, Renjun Duan, Shuangqian Liu
In the paper, we develop spectral theory to analyze the sharp asymptotic behavior of solutions to the Boltzmann equation around global Maxwellians in a three-dimensional infinite l…
The non-cutoff Vlasov-Poisson-Boltzmann system with weak collisions
Yuanjie Lei, Shuangqian Liu, Qinghua Xiao +1
We prove global existence of smooth solutions near Maxwellians for the non-cutoff Vlasov-Poisson-Boltzmann system in the weakly collisional regime. To address the weak dissipation…
Global stability of the inhomogeneous sheared Boltzmann equation in torus
Renjun Duan, Shuangqian Liu, Shunlin Shen
Homo-energetic solutions to the spatially homogeneous Boltzmann equation have been extensively studied, but their global stability in the inhomogeneous setting remains challenging…
The spatially inhomogeneous Vlasov-Nordström-Fokker-Planck system in the intrinsic weak diffusion regime
Shengchuang Chang, Shuangqian Liu, Tong Yang
The spatially homogeneous Vlasov-Nordström-Fokker-Planck system is known to exhibit nontrivial large time behavior, naturally leading to weak diffusion of the Fokker-Planck operato…
The 3D kinetic Couette flow via the Boltzmann equation in the diffusive limit
Renjun Duan, Shuangqian Liu, Robert M. Strain +1
In the paper we study the Boltzmann equation in the diffusive limit in a channel domain for the 3D kinetic Couette flow. Our results demonstrate that th…
Global Hilbert expansion for some non-relativistic kinetic equations
Yuanjie Lei, Shuangqian Liu, Qinghua Xiao +1
The Vlasov-Maxwell-Landau (VML) system and the Vlasov-Maxwell-Boltzmann (VMB) system are fundamental models in dilute collisional plasmas. In this paper, we are concerned with the…
Compressible Navier-Stokes approximation for the Boltzmann equation in bounded domains
Renjun Duan, Shuangqian Liu
It is well known that the full compressible Navier-Stokes equations can be deduced via the Chapman-Enskog expansion from the Boltzmann equation as the first-order correction to the…
Global stability of the rarefaction wave of the Vlasov-Poisson-Boltzmann system
Renjun Duan, Shuangqian Liu
This paper is devoted to the study of the nonlinear stability of the rarefaction waves of the Vlasov-Poisson-Boltzmann system with slab symmetry in the case where the electron back…