8 papers
Time-periodic solutions of the Vlasov-Poisson-Boltzmann system with a general external force in
Renjun Duan, Jinkai Ni
In this paper, we study the time-periodic problem for the Vlasov-Poisson-Boltzmann (VPB) system with a given time-periodic external force in the whole space . The for…
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.…
Half-space problem on the Boltzmann equation with zero Mach number at infinity
Hongxu Chen, Jun-ling Chen, Renjun Duan
We study the long-time dynamics of the time-evolutionary Boltzmann equation with hard sphere collisions in the three-dimensional half-space \( \mathbb{R}^2 \times \mathbb{R}^+\), s…
Three-dimensional time-periodic problem on the Boltzmann equation with external force
Renjun Duan, Jinkai Ni
The time-periodic problem on the Boltzmann equation with a given time-periodic external force in the three-dimensional whole space has remained open since it was first studied in […
Diffusive limit of the Boltzmann equation around Rayleigh profile in the half space
Hongxu Chen, Renjun Duan
This paper concerns the diffusive limit of the time evolutionary Boltzmann equation in the half space for a small Knudsen number . F…
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…