On the blowup of solutions for a nonlocal multi-dimensional transport equation
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866912932776902656 |
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| author | Zhang, Wanwan |
| author_facet | Zhang, Wanwan |
| contents | In this paper, we revisit the problem of finite-time blowup for a multi-dimensional nonlocal transport equation studied in [Dong, Adv. Math. 264 (2014) 747-761]. Inspired by a one-dimensional analogous model considered in [Li-Rodrigo, Adv. Math. 374 (2020) 1-26], we establish a new weighted nonlinear inequality implying the blow-up by a completely real variable based technique. In particular, an inequality for the Riesz transform is obtained. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_06449 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the blowup of solutions for a nonlocal multi-dimensional transport equation Zhang, Wanwan Analysis of PDEs In this paper, we revisit the problem of finite-time blowup for a multi-dimensional nonlocal transport equation studied in [Dong, Adv. Math. 264 (2014) 747-761]. Inspired by a one-dimensional analogous model considered in [Li-Rodrigo, Adv. Math. 374 (2020) 1-26], we establish a new weighted nonlinear inequality implying the blow-up by a completely real variable based technique. In particular, an inequality for the Riesz transform is obtained. |
| title | On the blowup of solutions for a nonlocal multi-dimensional transport equation |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2403.06449 |