Regularity of stationary solutions to the linearized Boltzmann equations

2016/04/13 by I‐Kun Chen, Chen, I-Kun
Engineering · Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #Gas Dynamics and Kinetic Theory #Lattice Boltzmann Simulation Studies #Navier-Stokes equation solutions

paper · pdf · doi:10.48550/arxiv.1604.03653

openalex publication_date 2016/04/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider the regularity of stationary solutions to the linearized Boltzmann equations in bounded C¹ convex domains in ℝ³ for gases with cutoff hard potential and cutoff Maxwellian gases. We prove that the stationary solutions solutions are Hölder continuous with order \frac12^- away from the boundary provided the incoming data have the same regularity. The key idea is to partially transfer the regularity in velocity obtained by collision to space through transport and collision.

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