Strong diffusive limit of the Boltzmann equation with Maxwell boundary condition

2018/09/18 by Yan Guo, Guo, Yan, Jung, Junhwa +1 · 3 citations
Mathematics · Physics and Astronomy · Engineering · #Gas Dynamics and Kinetic Theory #Advanced Thermodynamics and Statistical Mechanics #Fluid Dynamics and Turbulent Flows

paper · pdf · doi:10.48550/arxiv.1809.06763

Abstract

While weak diffusive limit from the Boltzmann equation to the incompressible Navier-Stokes-Fourier system was established for the Maxwell boundary condition within renormalized solutions framework [Saint.Raymond2009][Jiang-Masmoudi2017], the corresponding strong diffusive limit has remained outstanding except when the accommodation coefficient α∼ ε^1/2 [Jiang-Masmoudi2017]. We establish global in time strong diffusive limit for all accommodation coefficients α∈ [0, 1] within strong solutions framework. The main novelties of our proof include: (1) a ε-stretching method for reduction to a single-bounce L^∞ estimate; (2) a dissipation estimate for a carefully constructed rotating Maxwellian in the near-specular regime α≪ ε.

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