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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/2401.09219 |
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| _version_ | 1866911760133390336 |
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| author | Zou, Mianlu Li, Qiang |
| author_facet | Zou, Mianlu Li, Qiang |
| contents | In this paper, we study the regularity criteria for the 3D Boussinesq equations in terms of one partial derivative of the velocity in Besov spaces. More precisely, it is proved that if the velocity $u$ holds $\int_{0}^{T}\| \partial_{3} u\|_{\dot{B}_{\infty,\infty}^{-r}}^{\frac{2}{1-r}}\mbox{d}t<\infty,\ with\ \ 0\leq r<1$, then the solution $(u, θ)$ is regular on $[0,T]$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_09219 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A regularity criterion for the 3D Boussinesq equations in homogeneous Besov spaces with negative indices Zou, Mianlu Li, Qiang Analysis of PDEs In this paper, we study the regularity criteria for the 3D Boussinesq equations in terms of one partial derivative of the velocity in Besov spaces. More precisely, it is proved that if the velocity $u$ holds $\int_{0}^{T}\| \partial_{3} u\|_{\dot{B}_{\infty,\infty}^{-r}}^{\frac{2}{1-r}}\mbox{d}t<\infty,\ with\ \ 0\leq r<1$, then the solution $(u, θ)$ is regular on $[0,T]$. |
| title | A regularity criterion for the 3D Boussinesq equations in homogeneous Besov spaces with negative indices |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2401.09219 |