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Compressible Euler limit from Boltzmann equation with complete diffusive boundary condition in half-space

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arxiv 2104.11964 v3 pith:A6G5XPUJ submitted 2021-04-24 math.AP

Ning Jiang , Yi-Long Luo , Shaojun Tang This is my paper · ORCID
classification math.AP
keywords boltzmannboundarycitecompletecompressibleconditiondiffusiveequation
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In this paper, we prove the compressible Euler limit from the Boltzmann equation with hard sphere collisional kernel and complete diffusive boundary condition in half-space by employing the Hilbert expansion which includes interior and Knudsen layers. This rigorously justifies the corresponding formal analysis in Sone's book \cite{Sone-2007-Book} in the context of short time smooth solutions, and also generalizes the classic Caflisch's result \cite{Caflish-1980-CPAM} to initial-boundary problem case.

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  1. Knudsen boundary layer equations with incoming boundary condition: full range of cutoff collision kernels and Mach numbers of the far field

    math.AP 2025-01 conditional novelty 6.0 of 10

    Existence, uniqueness, and exponential decay for Knudsen layer solutions with incoming data are established for the full range of cutoff kernels and all Mach numbers.

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