On particle systems and critical strengths of general singular interactions
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866929446264504320 |
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| author | Kinzebulatov, Damir |
| author_facet | Kinzebulatov, Damir |
| contents | For finite interacting particle systems with strong repulsing-attracting or general interactions, we prove global weak well-posedness almost up to the critical threshold of the strengths of attracting interactions (independent of the number of particles), and establish other regularity results, such as a heat kernel bound in the regions where strongly attracting particles are close to each other. Our main analytic instruments are a variant of De Giorgi's method in $L^p$ with appropriately chosen large $p$, and an abstract desingularization theorem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_17009 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On particle systems and critical strengths of general singular interactions Kinzebulatov, Damir Probability Analysis of PDEs For finite interacting particle systems with strong repulsing-attracting or general interactions, we prove global weak well-posedness almost up to the critical threshold of the strengths of attracting interactions (independent of the number of particles), and establish other regularity results, such as a heat kernel bound in the regions where strongly attracting particles are close to each other. Our main analytic instruments are a variant of De Giorgi's method in $L^p$ with appropriately chosen large $p$, and an abstract desingularization theorem. |
| title | On particle systems and critical strengths of general singular interactions |
| topic | Probability Analysis of PDEs |
| url | https://arxiv.org/abs/2402.17009 |