Basic Relation of Compressible Gas Dynamics

and Boltzmann Equation

The Boltzmann equation in the kinetic theory of gases is closely related to the Euler equations and Navier-Stokes equations for compressible fluids. We will start from the basics of Boltzmann equation and derive the fluid equations. The elementary properties of the fluid equations will then be described. There is little prerequisites for these introductory talks beyond the multi-variables calculus.

Boltzmann Equation and Shock Waves

The travelin waves for the Boltzmann equation are called the Boltzmann shocks. The stability of Boltzmann shocks can be studied by energy method and pointwise method. The latter method demands understanding of the Green’s functions for the linearized Boltzmann equation. As an application of the stability analysis, one can describe the zero dissipation limit of the Boltzmann solutions to the Euler solutions with shocks.