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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2409.17151 |
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| _version_ | 1866929515251367936 |
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| author | Rahmani, Anis Mennouni, Abdelaziz |
| author_facet | Rahmani, Anis Mennouni, Abdelaziz |
| contents | This work investigates the existence and uniqueness of local weak solutions for the d-dimensional $(d \geq 2)$ fractional magnetic Bénard system without thermal diffusion, integrating the Bénard equation and MHD system. For $κ= 0$ and $1 \leq α=β< 1 + \dfrac{d}{4}$, we establish that any starting conditions $(u_{0},B_{0})\in B_{2,1}^{1+\frac{d}{2}-2α}(\mathbb{R}^{d})$ and $θ_{0}\in B_{2,1}^{1+\frac{d}{2}-α}(\mathbb{R}^{d})$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_17151 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | New approach in the Besov space to the existence and uniqueness of solutions of the D-dimensional fractional magnetic Bénard system without thermal diffusion Rahmani, Anis Mennouni, Abdelaziz Analysis of PDEs This work investigates the existence and uniqueness of local weak solutions for the d-dimensional $(d \geq 2)$ fractional magnetic Bénard system without thermal diffusion, integrating the Bénard equation and MHD system. For $κ= 0$ and $1 \leq α=β< 1 + \dfrac{d}{4}$, we establish that any starting conditions $(u_{0},B_{0})\in B_{2,1}^{1+\frac{d}{2}-2α}(\mathbb{R}^{d})$ and $θ_{0}\in B_{2,1}^{1+\frac{d}{2}-α}(\mathbb{R}^{d})$. |
| title | New approach in the Besov space to the existence and uniqueness of solutions of the D-dimensional fractional magnetic Bénard system without thermal diffusion |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2409.17151 |