Relativistic Boltzmann Equation: Large Time Behavior and Finite Speed of Propagation

In this talk, we will study the asymptotic behavior of the relativistic Boltzmann equation in the whole space ${\mathbb{R}}^{3}_{x}$ under the closed to equilibrium setting. We obtained the existence, uniqueness and large time behavior of the solution without imposing any Sobolev regularity (both the spatial and velocity variables) on the initial data. Moreover, we recognize the finite speed of propagation of the solution, which reflects the difference in essence between the relativistic Boltzmann equation and the classical Boltzmann equation. This work is jointed with Prof. Yu-Chu Lin and Kung-Chien Wu.