Global solutions to Stokes-Magneto equations with fractional dissipations
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2023
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| _version_ | 1866918096597417984 |
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| author | Bae, Hantaek Kwon, Hyunwoo Shin, Jaeyong |
| author_facet | Bae, Hantaek Kwon, Hyunwoo Shin, Jaeyong |
| contents | In this paper, we investigate a Stokes-Magneto system with fractional diffusions. We first deal with the non-resistive case in $\mathbb{T}^{d}$ and establish the local and global well-posedness with initial magnetic field $\mathbf{b}_0\in H^{s}(\mathbb{T}^d)$. We also show the existence of a unique mild solution of the resistive case with initial data $\mathbf{b}_0$ in the critical $L^{p}(\mathbb{R}^d)$ space. Moreover, we show that $\|\mathbf{b}(t)\|_{L^{p}}$ converges to zero as $t\rightarrow\infty$ when the initial data is sufficiently small. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_03255 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Global solutions to Stokes-Magneto equations with fractional dissipations Bae, Hantaek Kwon, Hyunwoo Shin, Jaeyong Analysis of PDEs 35Q35, 76W05 In this paper, we investigate a Stokes-Magneto system with fractional diffusions. We first deal with the non-resistive case in $\mathbb{T}^{d}$ and establish the local and global well-posedness with initial magnetic field $\mathbf{b}_0\in H^{s}(\mathbb{T}^d)$. We also show the existence of a unique mild solution of the resistive case with initial data $\mathbf{b}_0$ in the critical $L^{p}(\mathbb{R}^d)$ space. Moreover, we show that $\|\mathbf{b}(t)\|_{L^{p}}$ converges to zero as $t\rightarrow\infty$ when the initial data is sufficiently small. |
| title | Global solutions to Stokes-Magneto equations with fractional dissipations |
| topic | Analysis of PDEs 35Q35, 76W05 |
| url | https://arxiv.org/abs/2310.03255 |