Compressible Euler limit from Boltzmann equation with complete diffusive boundary condition in half-space
Abstract
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 Sone-2007-Book in the context of short time smooth solutions, and also generalizes the classic Caflisch's result Caflish-1980-CPAM to initial-boundary problem case.
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