On regularity of a Kinetic Boundary layer

2024/06/11 by Hongxu Chen, Chen, Hongxu
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Differential Equations and Numerical Methods #FOS: Mathematics #Heat Transfer and Mathematical Modeling

paper · pdf · doi:10.48550/arxiv.2406.06916

openalex publication_date 2024/06/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the nonlinear steady Boltzmann equation in the half space, with phase transition and Dirichlet boundary condition. In particular, we study the regularity of the solution to the half-space problem in the situation that the gas is in contact with its condensed phase. We propose a novel kinetic weight and establish a weighted C¹ estimate under the spatial domain x∈ [0,∞), which is unbounded and not strictly convex. Additionally, we prove the W^1,p estimate without any weight for p<2.

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