Abstract

Boltzmann and Landau equations are the microscopic models of the gas dynamics and plasma physics respectively. In this talk, I will present some pointwise behaviours of their solutions. The results reveal the particle and fluid aspects of the equation. The fluid-like waves reveal the dissipative behaviours of the type of Navier-Stokes equation, which represents the long time behaviour of the solutions. The kinetic-like waves dominate the short time behaviour. The different smoothing mechanism of them will also be discussed.