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arXiv · 2610.40322

Relativistic collision geometry and global near-vacuum solutions at critical transverse regularity

Xinfeng Hu·Shuangqian Liu·Haoran Peng·Yi Zhou
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Abstract

We establish global well-posedness near vacuum for the relativistic Boltzmann equation with soft and hard potentials in the range $γ\in(-2,1]$. The initial data have critical Besov regularity of order $2/r$ in the transverse spatial variables for an admissible range of $r$ depending on $γ$, together with weighted integrability in the longitudinal and momentum variables. The proof combines a fixed-direction div--curl lemma with bilinear collision estimates. In particular, to control the gain term, we combine localization to spherical caps with energy-weighted angular estimates. The key relativistic estimate controls the singularity associated with the first component of the post-collisional relative velocity. These bounds yield the required time decay.

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Xinfeng Hu, Shuangqian Liu, Haoran Peng, Yi Zhou. 2026-10-29. Relativistic collision geometry and global near-vacuum solutions at critical transverse regularity. https://arxiv.org/abs/2610.40322

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