7 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 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…