On a multi-dimensional transport equation with nonlocal velocity and fractional dissipation
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2024
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866911888043933696 |
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| author | Zhang, Wanwan |
| author_facet | Zhang, Wanwan |
| contents | This paper aims to investigate a multi-dimensional transport equation with nonlocal velocity and fractional dissipation.The balance between the nonlinearity and dissipation gives rise to three different cases, namely the subcritical, critical and supercritical ranges. We study those three cases and obtain a set of results containing local well-posedness, global smoothness, eventual regularity and finite-time blowup of smooth solutions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_16364 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On a multi-dimensional transport equation with nonlocal velocity and fractional dissipation Zhang, Wanwan Analysis of PDEs This paper aims to investigate a multi-dimensional transport equation with nonlocal velocity and fractional dissipation.The balance between the nonlinearity and dissipation gives rise to three different cases, namely the subcritical, critical and supercritical ranges. We study those three cases and obtain a set of results containing local well-posedness, global smoothness, eventual regularity and finite-time blowup of smooth solutions. |
| title | On a multi-dimensional transport equation with nonlocal velocity and fractional dissipation |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2405.16364 |