A bilinear fractional integral operator for Euler-Riesz systems
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866917549720993792 |
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| author | Alves, Nuno J. Grafakos, Loukas Tzavaras, Athanasios E. |
| author_facet | Alves, Nuno J. Grafakos, Loukas Tzavaras, Athanasios E. |
| contents | We establish a uniform estimate for a bilinear fractional integral operator via restricted weak-type endpoint estimates and Marcinkiewicz interpolation. This estimate is crucial in the integrability analysis of a tensor-valued bilinear fractional integral operator associated with Euler-Riesz systems modeling mean-field interactions induced by a singular kernel. The tensorial operator arises from a reformulation of the Euler-Riesz system that yields a gain in integrability for finite energy solutions through compensated integrability. Additionally, for smooth periodic solutions of the reformulated system, we derive a stability result. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2409_18309 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A bilinear fractional integral operator for Euler-Riesz systems Alves, Nuno J. Grafakos, Loukas Tzavaras, Athanasios E. Analysis of PDEs 42B20, 42B37, 35Q35 We establish a uniform estimate for a bilinear fractional integral operator via restricted weak-type endpoint estimates and Marcinkiewicz interpolation. This estimate is crucial in the integrability analysis of a tensor-valued bilinear fractional integral operator associated with Euler-Riesz systems modeling mean-field interactions induced by a singular kernel. The tensorial operator arises from a reformulation of the Euler-Riesz system that yields a gain in integrability for finite energy solutions through compensated integrability. Additionally, for smooth periodic solutions of the reformulated system, we derive a stability result. |
| title | A bilinear fractional integral operator for Euler-Riesz systems |
| topic | Analysis of PDEs 42B20, 42B37, 35Q35 |
| url | https://arxiv.org/abs/2409.18309 |