2021/01/27 by Ning Jiang, Jiang, Ning, Yi-Long Luo +3
Engineering · Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #Fluid Dynamics and Turbulent Flows #Gas Dynamics and Kinetic Theory #Navier-Stokes equation solutions
paper · pdf · doi:10.48550/arxiv.2101.11199
openalex publication_date 2021/01/27 · openalex created_date 2021/02/01 · openalex updated_date 2026/07/28
Starting from the local-in-time classical solution to the compressible Euler system with impermeable boundary condition in half-space, by employing the coupled weak viscous layers (governed by linearized compressible Prandtl equations with Robin boundary condition) and linear kinetic boundary layers, and the analytical tools in \citeGuo-Jang-Jiang-2010-CPAM and some new boundary estimates both for Prandtl and Knudsen layers, we proved the local-in-time existence of Hilbert expansion type classical solutions to the scaled Boltzmann equation with Maxwell reflection boundary condition with accommodation coefficient αε=O(√(ε)) when the Knudsen number ε small enough. As a consequence, this justifies the corresponding case of formal analysis in Sone's books \citeSone-2002book, Sone-2007-Book. This also extends the results in \citeGHW-2020 from specular to Maxwell reflection boundary condition. Both of this paper and \citeGHW-2020 can be viewed as generalizations of Caflisch's classic work \citeCaflish-1980-CPAM to the cases with boundary.