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arXiv · 2001.11672

Propagation of $L^p$ estimates for the Spatially Homogeneous Relativistic Boltzmann Equation

Jin Woo Jang·Seok-Bae Yun
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Abstract

In this paper, we prove the propagation of $L^p$ upper bounds for the spatially homogeneous relativistic Boltzmann equation for any $1<p<\infty$. We consider the case of relativistic \textit{hard ball} with Grad's angular cutoff. Our proof is based on a detailed study of the interrelationship between the relative momenta, the regularity and the $L^p$ estimates for the gain operator, the development of the relativistic Carleman representation, and several estimates on the relativistic hypersurface $E^{v_*}_{v'-v}$. We also derive a Pythagorean theorem for the \textit{relative momenta} $g(v,v_*),$ $g(v,v')$, and $g(v',v_*)$, which has a crucial role in the reduction of the momentum singularity.

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Jin Woo Jang, Seok-Bae Yun. 2020-01-31. Propagation of $L^p$ estimates for the Spatially Homogeneous Relativistic Boltzmann Equation. https://arxiv.org/abs/2001.11672

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