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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2403.15613 |
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| _version_ | 1866913914465288192 |
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| author | Alonso, Ricardo J. Gervais, Pierre Lods, Bertrand |
| author_facet | Alonso, Ricardo J. Gervais, Pierre Lods, Bertrand |
| contents | We introduce a practical criterion that justifies the propagation and appearance of $L^{p}$-norms for the solutions to the spatially homogeneous Boltzmann equation with very soft potentials without cutoff. Such criterion also provides a new conditional stability result for classical solutions to the equation. All results are quantitative. Our approach is inspired by a recent analogous result for the Landau equation derived in arXiv:2306.15729 and generalises existing conditional results related to higher integrability properties and stability of solutions to the Boltzmann equation with very soft potentials. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_15613 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Conditional integrability and stability for the homogeneous Boltzmann equation with very soft potentials Alonso, Ricardo J. Gervais, Pierre Lods, Bertrand Analysis of PDEs We introduce a practical criterion that justifies the propagation and appearance of $L^{p}$-norms for the solutions to the spatially homogeneous Boltzmann equation with very soft potentials without cutoff. Such criterion also provides a new conditional stability result for classical solutions to the equation. All results are quantitative. Our approach is inspired by a recent analogous result for the Landau equation derived in arXiv:2306.15729 and generalises existing conditional results related to higher integrability properties and stability of solutions to the Boltzmann equation with very soft potentials. |
| title | Conditional integrability and stability for the homogeneous Boltzmann equation with very soft potentials |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2403.15613 |