2020/08/24 by Lei Wu, Wu, Lei, Zhimeng Ouyang +1
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Gas Dynamics and Kinetic Theory #Lattice Boltzmann Simulation Studies
paper · pdf · doi:10.48550/arxiv.2008.10507
openalex publication_date 2020/08/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/31
Consider 3D Boltzmann equation in convex domains with diffusive-reflection boundary condition. We study the hydrodynamic limits as the Knudsen number and Strouhal number ε→ 0+. Using the Hilbert expansion, we rigorously justify that the solution of stationary/evolutionary problem converges to that of the steady/unsteady Navier-Stokes-Fourier system. This is the first paper to justify the hydrodynamic limits of nonlinear Boltzmann equations with hard-sphere collision kernel in bounded domain in the L∞ sense. The proof relies on a novel analysis on the boundary layer effect with geometric correction. The difficulty mainly comes from three sources: 3D domain, boundary layer regularity, and time dependence. To fully solve this problem, we introduce several techniques: (1) boundary layer with geometric correction; (2) remainder estimates with L2-L6-L∞ framework. Keywords: boundary layer; Milne problem; geometric correction; remainder estimates.