Uniform L²-stability estimates for the relativistic Boltzmann equation

In this paper, we derive an a priori L²-stability estimate for classical solutions to the relativistic Boltzmann equation, when the initial datum is a small perturbation of a global relativistic Maxwellian. For the stability estimate, we use the dissipative property of the linearized collision operator and a Strichartz type estimate for classical solutions. As a direct application of our stability estimates, we establish that classical solutions in Glassey-Strauss and Hsiao-Yu's frameworks satisfy a uniform L²-stability estimate.