The Landau equation does not blow up
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866909467587641344 |
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| author | Guillen, Nestor Silvestre, Luis |
| author_facet | Guillen, Nestor Silvestre, Luis |
| contents | We consider solutions to the space-homogeneous Landau equation with a general family of interaction potentials. We prove that their Fisher information is monotone decreasing in time. The class of interaction potentials covered by our result includes the case of the Landau equation with Coulomb interactions. As a consequence of the global boundedness of the Fisher information, we deduce that solutions to the space-homogeneous Landau equation never blow up. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_09420 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | The Landau equation does not blow up Guillen, Nestor Silvestre, Luis Analysis of PDEs 35Q70 We consider solutions to the space-homogeneous Landau equation with a general family of interaction potentials. We prove that their Fisher information is monotone decreasing in time. The class of interaction potentials covered by our result includes the case of the Landau equation with Coulomb interactions. As a consequence of the global boundedness of the Fisher information, we deduce that solutions to the space-homogeneous Landau equation never blow up. |
| title | The Landau equation does not blow up |
| topic | Analysis of PDEs 35Q70 |
| url | https://arxiv.org/abs/2311.09420 |