21 citations · 38 across the 8 of their papers we have counts for
8 papers
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…
Macroscopic estimate of the linear Boltzmann and Landau equations with Specular reflection boundary
Hongxu Chen, Chanwoo Kim
In this short note, we prove an -control of the macroscopic part of the linear Boltzmann and Landau equations. This result is an extension of the test function method of Espos…
Gradient Decay in the Boltzmann theory of Non-isothermal boundary
Hongxu Chen, Chanwoo Kim
We consider the Boltzmann equation in convex domain with non-isothermal boundary of diffuse reflection. For both unsteady/steady problems, we construct solutions belong to $W^{1,p}…
Regularity of Boltzmann equation with Cercignani-Lampis boundary in convex domain
Hongxu Chen
The Boltzmann equation is a fundamental kinetic equation that describes the dynamics of dilute gas. In this paper we study the regularity of both dynamical and steady Boltzmann equ…
Local Well-posedness of Vlasov-Poisson-Boltzmann Equation with Generalized Diffuse Boundary Condition
Hongxu Chen, Chanwoo Kim, Qin Li
The Vlasov-Poisson-Boltzmann equation is a classical equation governing the dynamics of charged particles with the electric force being self-imposed. We consider the system in a co…
Regularity of Stationary Boltzmann equation in Convex Domains
Hongxu Chen, Chanwoo Kim
Higher regularity estimate has been a challenging question for the Boltzmann equation in bounded domains. Indeed, it is well-known to have "the non-existence of a second order deri…
Cercignani-Lampis boundary in the Boltzmann theory
Hongxu Chen
The Boltzmann equation is a fundamental kinetic equation that describes the dynamics of dilute gas. In this paper we study the local well-posedness of the Boltzmann equation in bou…
A Numerical method for coupling the BGK model and Euler equation through the linearized Knudsen layer
Hongxu Chen, Qin Li, Jianfeng Lu
The Bhatnagar-Gross-Krook (BGK) model, a simplification of the Boltzmann equation, in the absence of boundary effect, converges to the Euler equations when the Knudsen number is sm…