Quantitative relaxation towards equilibrium for solutions to the Boltzmann-Fermi-Dirac equation with cutoff hard potentials
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866916121394806784 |
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| author | Borsoni, Thomas Lods, Bertrand |
| author_facet | Borsoni, Thomas Lods, Bertrand |
| contents | We provide the first quantitative result of convergence to equilibrium in the context of the spatially homogeneous Boltzmann-Fermi-Dirac equation associated to hard potentials interactions under angular cut-off assumption, providing an explicit - algebraic - rate of convergence to Fermi-Dirac steady solutions. This result complements the quantitative convergence result of Liu and Lu and is based upon new uniform-in-time-and-$\varepsilon$ $L^{\infty}$ bound on the solutions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_06807 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Quantitative relaxation towards equilibrium for solutions to the Boltzmann-Fermi-Dirac equation with cutoff hard potentials Borsoni, Thomas Lods, Bertrand Analysis of PDEs Mathematical Physics We provide the first quantitative result of convergence to equilibrium in the context of the spatially homogeneous Boltzmann-Fermi-Dirac equation associated to hard potentials interactions under angular cut-off assumption, providing an explicit - algebraic - rate of convergence to Fermi-Dirac steady solutions. This result complements the quantitative convergence result of Liu and Lu and is based upon new uniform-in-time-and-$\varepsilon$ $L^{\infty}$ bound on the solutions. |
| title | Quantitative relaxation towards equilibrium for solutions to the Boltzmann-Fermi-Dirac equation with cutoff hard potentials |
| topic | Analysis of PDEs Mathematical Physics |
| url | https://arxiv.org/abs/2402.06807 |