Uniform L¹-stability of the relativistic Boltzmann equation near vacuum

We present the uniform L¹-stability estimate for the relativistic Boltzmann equation near vacuum. For this, we explicitly construct a relativistic counterpart of the nonlinear functional which is a linear combination of L¹-distance and a collision potential. This functional measures the L¹-distance between two continuous mild solutions. When the initial data is sufficiently small and decays exponentially fast, we show that the functional satisfies the uniform stability estimate leading to the uniform L¹-stability estimate with respect to initial data.