arXiv subjects

Ping-Han Chuang

Publications and source records attributed to Ping-Han Chuang.

2 recordsLinked to original sources

arXiv2023

On the Existence of $H^1$ solutions for Stationary Linearized Boltzmann Equations in a Small Convex Domain

In this article, we investigate the incoming boundary value problem for the stationary linearized Boltzmann equations in $ \Omega \subseteq \mathbb{R}^{3}$. For a $C^2$ bounded domain with boundary of positive Gaussian curvature, the existence theory is established in $H^{1}(\Omega \times \mathbb{R}^{3})$ provided that the diameter of the domain $\Omega$ is small enough.

math.AP↗

arXiv2020

A Revisit of the Velocity Averaging Lemma: on the Regularity of Stationary Boltzmann Equation in a Bounded Convex Domain

In the present work, we adopt the idea of velocity averaging lemma to establish regularity for stationary linearized Boltzmann equations in a bounded convex domain. Considering the incoming data, with three iterations, we establish regularity in fractional Sobolev space in space variable up to order $1^-$.

math.AP↗