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Local Hilbert expansion for the Boltzmann equation

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  • We revisit the classical work of Caflisch [1] for compressible Euler limit of the Boltzmann equation. By using a new $L^{2}\mbox{-}L^{\infty }$ method, we prove the validity of the Hilbert expansion before shock formations in the Euler system with moderate temperature variation.
    Mathematics Subject Classification: Primary: 76P05, 35L67; Secondary: 82A40.

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