Propagation of L^p estimates for the spatially homogeneous relativistic Boltzmann equation

Abstract

In this paper, we prove the propagation of Lp upper bounds for the spatially homogeneous relativistic Boltzmann equation for any 1<p<∞. We consider the case of relativistic hard ball with Grad&apos;s angular cutoff. Our proof is based on a detailed study of the inter-relationship between the relative momenta, the regularity and the Lp estimates for the gain operator, the development of the relativistic Carleman representation, and several estimates on the relativistic hypersurface Evv. We also derive a Pythagorean theorem for the relative momenta g(v,v⁎), g(v,v′), and g(v′,v⁎), which has a crucial role in the reduction of the momentum singularity.