The Boltzmann equation with large-amplitude initial data and specular reflection boundary condition

2020/11/03 by Renjun Duan, Duan, Renjun, Gyounghun Ko +3
Engineering · Mathematics · #35Q20 #76P05 #Analysis of PDEs (math.AP) #Computational Fluid Dynamics and Aerodynamics #FOS: Mathematics #Gas Dynamics and Kinetic Theory #Numerical methods in inverse problems

paper · pdf · doi:10.48550/arxiv.2011.01503

openalex publication_date 2020/11/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For the Boltzmann equation with cutoff hard potentials, we construct the unique global solution converging with an exponential rate in large time to global Maxwellians not only for the specular reflection boundary condition with the bounded convex C³ domain but also for a class of large amplitude initial data where the Lⁱnfty norm with a suitable velocity weight can be arbitrarily large but the relative entropy need to be small. A key point in the proof is to introduce a delicate nonlinear iterative process of estimating the gain term basing on the triple Duhamel iteration along the linearized dynamics.

Citations

• Strong diffusive limit of the Boltzmann equation with Maxwell boundary condition

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