Boltzmann equation and conservation laws in gas dynamics

Tai-Ping Liu Stanford University and Academia Sinica (Taiwan)

There has been important progresses in recent years in the theory of shock waves for coservation laws. We will discuss the recent efforts on the Navier-Stokes equations in gas dynamics and Boltzmann equation in kinetic theory. The relationship between these equations has been much studied in two directions: One is for the incompressible limits and the other is for compressible shockless flows. We will view the Boltzmann equation via the compressible Euler and Navier-Stokes equations. This viewpoint yields new setup and analytical possibilities, which we will illustrate with the stability problem for shock and diffusion waves for the Boltzmann equation.