Global smooth solutions to the irrotational Euler-Riesz system in three dimensions
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866913629191798784 |
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| author | Choi, Young-Pil Jung, Jinwook Lee, Yoonjung |
| author_facet | Choi, Young-Pil Jung, Jinwook Lee, Yoonjung |
| contents | This paper investigates the global dynamics of the Euler--Riesz system in three dimensions, focusing on the well-posedness and large-time behavior of solutions near equilibrium. The system generalizes classical interactions by incorporating the Riesz interactions $\nabla (-Δ)^{-σ/2}(ρ- 1)$. We show that the system admits a global smooth solution for small irrotational initial perturbations. Specifically, we establish that if the initial data is sufficiently small, the solution remains regular globally in time and decays over time at a rate dependent on $σ$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_20705 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Global smooth solutions to the irrotational Euler-Riesz system in three dimensions Choi, Young-Pil Jung, Jinwook Lee, Yoonjung Analysis of PDEs 35Q31, 76N10 This paper investigates the global dynamics of the Euler--Riesz system in three dimensions, focusing on the well-posedness and large-time behavior of solutions near equilibrium. The system generalizes classical interactions by incorporating the Riesz interactions $\nabla (-Δ)^{-σ/2}(ρ- 1)$. We show that the system admits a global smooth solution for small irrotational initial perturbations. Specifically, we establish that if the initial data is sufficiently small, the solution remains regular globally in time and decays over time at a rate dependent on $σ$. |
| title | Global smooth solutions to the irrotational Euler-Riesz system in three dimensions |
| topic | Analysis of PDEs 35Q31, 76N10 |
| url | https://arxiv.org/abs/2412.20705 |