2022/10/10 by Feimin Huang, Weiqiang Wang, Huang, Feimin +5 · 1 citation
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Gas Dynamics and Kinetic Theory #Navier-Stokes equation solutions
paper · pdf · doi:10.48550/arxiv.2210.04616
openalex publication_date 2022/10/10 · openalex created_date 2022/10/12 · openalex updated_date 2026/07/28
The study of hydrodynamic limit of the Boltzmann equation with physical boundary is a challenging problem due to appearance of the viscous and Knudsen boundary layers. In this paper, the hydrodynamic limit from the Boltzmann equation with specular reflection boundary condition to the incompressible Euler in a channel is investigated. Based on the multiscaled Hilbert expansion, the equations with boundary conditions and compatibility conditions for interior solutions, viscous and Knudsen boundary layers are derived under different scaling, respectively. Then some uniform estimates for the interior solutions, viscous and Knudsen boundary layers are established. With the help of L2-L^∞ framework and the uniform estimates obtained above, the solutions to the Boltzmann equation are constructed by the truncated Hilbert expansion with multiscales, and hence the hydrodynamic limit in the incompressible Euler level is justified.