### From Boltzmann to Euler: Hilbert's 6th problem revisited.

Slemrod, M *(University of Wisconsin-Madison)*

Wednesday 05 March 2014, 15:15-16:15

Seminar Room 2, Newton Institute Gatehouse

#### Abstract

This talk addresses the hydrodynamic limit of the Boltzmann equation, namely
the compressible Euler equations of gas dynamics. An exact summation of the
Chapman-Enskog expansion originally given by Gorban and 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.