Local Hilbert expansion for the Boltzmann equation
Local Hilbert expansion for the Boltzmann equation
We revisit the classical work of Caflisch [1] for compressibleEuler limit of the Boltzmann equation. By using a new$L^{2}\mbox{-}L^{\infty }$ method, we prove the validity of theHilbert expansion before shock formations in the Euler system withmoderate temperature variation.