Local well-posedness for the Boltzmann equation with hard potentials

Hao-Guang Li; Wei-Xi Li; Chao-Jiang Xu

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arXiv · 2602.19148

Local well-posedness for the Boltzmann equation with hard potentials

Hao-Guang Li·Wei-Xi Li·Chao-Jiang Xu

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Abstract

We consider the spatially inhomogeneous non-cutoff Boltzmann equation with hard potentials in the non-perturbative setting. For initial data with polynomial decay in the velocity variable, we establish the local-in-time existence and uniqueness of weak solutions, conditional to pointwise bounds on the hydrodynamic quantities (mass, energy, and entropy). Compared to the soft potential case, the key challenge for full-range hard potentials lies in the more severe loss of velocity moments. The proof combines a hypoelliptic estimate with interpolation inequalities to handle the moment-loss terms.

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BibTeX RIS

Hao-Guang Li, Wei-Xi Li, Chao-Jiang Xu. 2026-02-22. Local well-posedness for the Boltzmann equation with hard potentials. https://arxiv.org/abs/2602.19148

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