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

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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.