The stochastic MHD equations driven by pure jump noise in $L^p$ spaces
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866912159722635264 |
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| author | Ni, Kaicheng Su, Heling Zhu, Jiahui |
| author_facet | Ni, Kaicheng Su, Heling Zhu, Jiahui |
| contents | We consider the stochastic incompressible magnetohydrodynamic equations driven by additive jump noises on either the whole space $\mathbb{R}^d$, $d=2,3$ or a smooth bounded domain $D$ in $\mathbb{R}^d$. We establish the local existence and uniqueness of a mild solution in the space $L^q(0,T;\mathbb{L}^{p\otimes}_σ(D))$ allowing for initial data with less regularity, including the marginal case $u_0\in \mathbb{L}^{d\otimes}_σ(D)$. In the two-dimensional case, we also prove the global existence of mild solutions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_12577 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The stochastic MHD equations driven by pure jump noise in $L^p$ spaces Ni, Kaicheng Su, Heling Zhu, Jiahui Probability Analysis of PDEs We consider the stochastic incompressible magnetohydrodynamic equations driven by additive jump noises on either the whole space $\mathbb{R}^d$, $d=2,3$ or a smooth bounded domain $D$ in $\mathbb{R}^d$. We establish the local existence and uniqueness of a mild solution in the space $L^q(0,T;\mathbb{L}^{p\otimes}_σ(D))$ allowing for initial data with less regularity, including the marginal case $u_0\in \mathbb{L}^{d\otimes}_σ(D)$. In the two-dimensional case, we also prove the global existence of mild solutions. |
| title | The stochastic MHD equations driven by pure jump noise in $L^p$ spaces |
| topic | Probability Analysis of PDEs |
| url | https://arxiv.org/abs/2412.12577 |