Local well-posedness for the Boltzmann equation with hard potentials
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866917286811533312 |
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| author | Li, Hao-Guang Li, Wei-Xi Xu, Chao-Jiang |
| author_facet | Li, Hao-Guang Li, Wei-Xi Xu, Chao-Jiang |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_19148 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Local well-posedness for the Boltzmann equation with hard potentials Li, Hao-Guang Li, Wei-Xi Xu, Chao-Jiang Analysis of PDEs 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. |
| title | Local well-posedness for the Boltzmann equation with hard potentials |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2602.19148 |