Nonlinear stability of planar rarefaction wave to the three-dimensional Boltzmann equation

2017/12/15 by Teng Wang, Yi Wang, Wang, Teng +1
Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Gas Dynamics and Kinetic Theory #Navier-Stokes equation solutions

paper · pdf · doi:10.48550/arxiv.1712.05489

openalex publication_date 2017/12/15 · openalex created_date 2019/06/27 · openalex updated_date 2026/07/28

Abstract

We investigate the time-asymptotic stability of planar rarefaction wave for the three-dimensional Boltzmann equation, based on the micro-macro decomposition introduced in [24, 22] and our new observations on the underlying wave structures of the equation to overcome the difficulties due to the wave propagation along the transverse directions and its interactions with the planar rarefaction wave. Note that this is the first stability result of planar rarefaction wave for 3D Boltzmann equation, while the corresponding results for the shock and contact discontinuities are still completely open.

Citations

• Hyperbolic systems of conservation laws II

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