Hydrodynamic limit of the Boltzmann equation to the planar rarefaction wave in three dimensional space

2019/10/14 by Guanfa Wang, Yong Wang, Wang, Guanfa +3
Engineering · Mathematics · #Analysis of PDEs (math.AP) #Computational Fluid Dynamics and Aerodynamics #FOS: Mathematics #Gas Dynamics and Kinetic Theory #Navier-Stokes equation solutions

paper · pdf · doi:10.48550/arxiv.1910.05890

openalex publication_date 2019/10/14 · openalex created_date 2019/10/18 · openalex updated_date 2026/07/28

Abstract

In this paper, we establish the global in time hydrodynamic limit of Boltzmann equation to the planar rarefaction wave of compressible Euler system in three dimensional space x∈ℝ³ for general collision kernels. Our approch is based on a generalized Hilbert expansion, and a recent L²-L^∞ framework. In particular, we improve the L²-estimate to be a localized version because the planar rarefaction wave is indeed a one-dimensional wave which makes the source terms to be not integrable in the L² energy estimate of three dimensional problem. We also point out that the wave strength of rarefaction may be large.

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