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

  • * Corresponding author: Yi Wang

    * Corresponding author: Yi Wang

The first author is supported by NSFC Grant No. 11601031. The second author is supported by NSFC grants No. 11671385 and 11688101 and CAS Interdisciplinary Innovation Team

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  • 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.

    Mathematics Subject Classification: Primary: 35Q20, 76P05, 74J40; Secondary: 35L65.


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