Asymptotic Stability of the Relativistic Boltzmann Equation for the Soft Potentials
Abstract
In this paper it is shown that unique solutions to the relativistic Boltzmann equation exist for all time and decay with any polynomial rate towards their steady state relativistic Maxwellian provided that the initial data starts out sufficiently close in $${L^\infty_\ell}$$. If the initial data are continuous then so is the corresponding solution. We work in the case of a spatially periodic box. Conditions on the collision kernel are generic in the sense of Dudyński and Ekiel-Jeżewska (Commun Math Phys 115(4):607-629, 1985); this resolves the open question of global existence for the soft potentials.
- Publication:
-
Communications in Mathematical Physics
- Pub Date:
- December 2010
- DOI:
- 10.1007/s00220-010-1129-1
- arXiv:
- arXiv:1003.4893
- Bibcode:
- 2010CMaPh.300..529S
- Keywords:
-
- Boltzmann Equation;
- Asymptotic Stability;
- Mild Solution;
- Collision Operator;
- Energy Inequality;
- Mathematics - Analysis of PDEs;
- Mathematical Physics
- E-Print:
- 64 pages