2024/11/26 by Hongxu Chen, Renjun Duan, Chen, Hongxu +3 · 2 citations
Engineering · Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #Fluid Dynamics and Turbulent Flows #Gas Dynamics and Kinetic Theory #Particle Dynamics in Fluid Flows
paper · pdf · doi:10.48550/arxiv.2411.17068
openalex publication_date 2024/11/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let rarefied gas be confined in an infinite layer with diffusely reflecting boundaries that are isothermal and non-moving. The initial-boundary value problem on the nonlinear Boltzmann equation governing the rarefied gas flow in such setting is challenging due to unboundedness of both domain and its boundaries as well as the presence of physical boundary conditions. In the paper, we establish the global-in-time dynamics of such rarefied gas flows near global Maxwellians in three or two-dimensions. For the former case, we also prove that the solutions decay in time at a polynomial rate which is the same as that of solutions to the two-dimensional heat equation. This is the first result on global solutions of the Boltzmann equation with non-compact and diffuse boundaries.