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.
Compressible Euler limit from Boltzmann equation with complete diffusive boundary condition in half-space
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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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Knudsen boundary layer equations with incoming boundary condition: full range of cutoff collision kernels and Mach numbers of the far field
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.