From Boltzmann to Euler: Hilbert's 6th Problem Revisited

Beautiful stuff!!

From Boltzmann to Euler: Hilbert's 6th Problem Revisited

Marshall Slemrod

This article addresses the hydrodynamic limit of the Boltzmann equation to
the compressible Euler equations of gas dynamics. An exact summation of
the Chapman-Enskog expansion originally given by A. Gorban and I. Karlin
is the key to the analysis. An appraisal of the role of viscosity and capillarity
in the limiting process is then given where the analogy is drawn to the limit
of the Korteweg - de Vries - Burgers equations as a small parameter tends
to zero.