Abstract
The spatially homogeneous Boltzmann equation has been studied extensively in the Newtonian case, but not much is known for the special relativistic case. In this paper, we address several issues for the spatially homogeneous Boltzmann equation for relativistic particles. We first derive the relativistic version of the Povzner inequality. Using this, we study the Cauchy problem and investigate how the polynomial and exponential moments in L1 are propagated. Several key differences between the relativistic and the Newtonian cases are confronted and discussed.
| Original language | English |
|---|---|
| Pages (from-to) | 917-938 |
| Number of pages | 22 |
| Journal | SIAM Journal on Mathematical Analysis |
| Volume | 46 |
| Issue number | 1 |
| DOIs | |
| State | Published - 2014 |
Keywords
- Boltzmann equation
- Kinetic theory of gases
- Moment estimates
- Povzner inequality
- Special relativity