$L^p$-norms for the homogeneous non-cutoff Boltzmann equation with soft potentials
Fuente:
arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866909217162526720 |
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| author | Spragge, Matt Sun, Weiran |
| author_facet | Spragge, Matt Sun, Weiran |
| contents | We establish a priori estimates showing the propagation and generation of $L^p$-norms for solutions to the non-cutoff spatially homogeneous Boltzmann equation with soft potentials. The singularity of the collision kernel is key to generate regularization and inhomogeneity in the energy estimates of the $L^p$-norms. Our result extends \cite{Alo19} from the hard potential cases to the soft ones. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_02813 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | $L^p$-norms for the homogeneous non-cutoff Boltzmann equation with soft potentials Spragge, Matt Sun, Weiran Analysis of PDEs We establish a priori estimates showing the propagation and generation of $L^p$-norms for solutions to the non-cutoff spatially homogeneous Boltzmann equation with soft potentials. The singularity of the collision kernel is key to generate regularization and inhomogeneity in the energy estimates of the $L^p$-norms. Our result extends \cite{Alo19} from the hard potential cases to the soft ones. |
| title | $L^p$-norms for the homogeneous non-cutoff Boltzmann equation with soft potentials |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2406.02813 |